@article{SchoppaSiegVogeletal.2020, author = {Schoppa, Lukas and Sieg, Tobias and Vogel, Kristin and Z{\"o}ller, Gert and Kreibich, Heidi}, title = {Probabilistic flood loss models for companies}, series = {Water resources research}, volume = {56}, journal = {Water resources research}, number = {9}, publisher = {American Geophysical Union}, address = {Washington}, issn = {0043-1397}, doi = {10.1029/2020WR027649}, pages = {19}, year = {2020}, abstract = {Flood loss modeling is a central component of flood risk analysis. Conventionally, this involves univariable and deterministic stage-damage functions. Recent advancements in the field promote the use of multivariable and probabilistic loss models, which consider variables beyond inundation depth and account for prediction uncertainty. Although companies contribute significantly to total loss figures, novel modeling approaches for companies are lacking. Scarce data and the heterogeneity among companies impede the development of company flood loss models. We present three multivariable flood loss models for companies from the manufacturing, commercial, financial, and service sector that intrinsically quantify prediction uncertainty. Based on object-level loss data (n = 1,306), we comparatively evaluate the predictive capacity of Bayesian networks, Bayesian regression, and random forest in relation to deterministic and probabilistic stage-damage functions, serving as benchmarks. The company loss data stem from four postevent surveys in Germany between 2002 and 2013 and include information on flood intensity, company characteristics, emergency response, private precaution, and resulting loss to building, equipment, and goods and stock. We find that the multivariable probabilistic models successfully identify and reproduce essential relationships of flood damage processes in the data. The assessment of model skill focuses on the precision of the probabilistic predictions and reveals that the candidate models outperform the stage-damage functions, while differences among the proposed models are negligible. Although the combination of multivariable and probabilistic loss estimation improves predictive accuracy over the entire data set, wide predictive distributions stress the necessity for the quantification of uncertainty.}, language = {en} } @article{SchroeterRitterHolschneideretal.2016, author = {Schroeter, M-A and Ritter, M. and Holschneider, Matthias and Sturm, H.}, title = {Enhanced DySEM imaging of cantilever motion using artificial structures patterned by focused ion beam techniques}, series = {Journal of micromechanics and microengineering}, volume = {26}, journal = {Journal of micromechanics and microengineering}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0960-1317}, doi = {10.1088/0960-1317/26/3/035010}, pages = {7}, year = {2016}, abstract = {We use a dynamic scanning electron microscope (DySEM) to map the spatial distribution of the vibration of a cantilever beam. The DySEM measurements are based on variations of the local secondary electron signal within the imaging electron beam diameter during an oscillation period of the cantilever. For this reason, the surface of a cantilever without topography or material variation does not allow any conclusions about the spatial distribution of vibration due to a lack of dynamic contrast. In order to overcome this limitation, artificial structures were added at defined positions on the cantilever surface using focused ion beam lithography patterning. The DySEM signal of such high-contrast structures is strongly improved, hence information about the surface vibration becomes accessible. Simulations of images of the vibrating cantilever have also been performed. The results of the simulation are in good agreement with the experimental images.}, language = {en} } @unpublished{Schrohe2000, author = {Schrohe, Elmar}, title = {A short introduction to Boutet de Monvel's calculus}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25696}, year = {2000}, abstract = {This paper provides an introduction to Boutet de Monvel's calculus on the half-space IRn (positiv) in the framework of a pseudodifferential calculus with operator-valued symbols.}, language = {en} } @unpublished{Schrohe1999, author = {Schrohe, Elmar}, title = {Noncommutative residues, Dixmier's Trace, and heat trace expansions on manifolds with boundary}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25486}, year = {1999}, abstract = {For manifolds with boundary, we define an extension of Wodzicki's noncommutative residue to boundary value problems in Boutet de Monvel's calculus. We show that this residue can be recovered with the help of heat kernel expansions and explore its relation to Dixmier's trace.}, language = {en} } @misc{Schrohe1998, author = {Schrohe, Elmar}, title = {Wloka, J. T. [u.a.], Boundary value problems for eliptic systems}, year = {1998}, language = {en} } @article{Schrohe1997, author = {Schrohe, Elmar}, title = {Noncommutative residue and manifolds with conicial singularities}, year = {1997}, language = {en} } @article{Schrohe1997, author = {Schrohe, Elmar}, title = {Wodzicki{\"i}s noncommutative residue and trace for operator algebras on manifolds with conical singularities}, year = {1997}, language = {en} } @misc{Schrohe1995, author = {Schrohe, Elmar}, title = {Schulze, B.-W., Pseudo-Differential Boundary Value Problems, Conical Singularities, and Asymptotics; Berlin, Akademie-Verl., 1995}, year = {1995}, language = {en} } @article{Schrohe1996, author = {Schrohe, Elmar}, title = {Traces on the cone algebra with asymptotics}, year = {1996}, language = {en} } @misc{Schrohe1998, author = {Schrohe, Elmar}, title = {Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods}, year = {1998}, language = {en} } @article{Schrohe2001, author = {Schrohe, Elmar}, title = {A short introduction to Boutet de Monvel's calculus}, year = {2001}, language = {en} } @article{Schrohe2001, author = {Schrohe, Elmar}, title = {Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces}, year = {2001}, language = {en} } @book{Schrohe2000, author = {Schrohe, Elmar}, title = {A short introduction to Boutet de Monvel`s calculus}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {23 S. : graph. Darst.}, year = {2000}, language = {en} } @misc{Schrohe1999, author = {Schrohe, Elmar}, title = {Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods}, year = {1999}, language = {en} } @article{Schrohe1999, author = {Schrohe, Elmar}, title = {Frechet algebra techniques for boundary value problems on noncompact manifolds : Fredholm riteria and functional calculus via spectral invariance}, year = {1999}, language = {en} } @article{Schrohe1999, author = {Schrohe, Elmar}, title = {Noncommutative residues, Diximier{\"i}s trace, and heat trace expansions on manifolds with boundary}, year = {1999}, language = {en} } @article{SchroheHieber1999, author = {Schrohe, Elmar and Hieber, Matthias}, title = {Lp spectral independence of elliptic operators via commutator estimates}, year = {1999}, language = {en} } @article{SchroheLeopold1997, author = {Schrohe, Elmar and Leopold, H.-G.}, title = {Invariance of the LP spectrum for hypoeliptic operators}, year = {1997}, language = {en} } @article{SchroheNest1998, author = {Schrohe, Elmar and Nest, R.}, title = {Diximier{\"i}s trace for boundary value problems}, year = {1998}, language = {en} } @unpublished{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Edge-degenerate boundary value problems on cones}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25436}, year = {1999}, abstract = {We consider edge-degenerate families of pseudodifferential boundary value problems on a semi-infinite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near infinity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.}, language = {en} } @book{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Edge-degenerate boundary value problems on cones}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {14 S.}, year = {1999}, language = {en} } @article{SchroheSchulze1995, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Boundary value problems in Boutet de Monvel's algebra for manifolds with conical singularities II}, year = {1995}, language = {en} } @article{SchroheSchulze1994, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Boundary value problems in Boutet de Monvel{\"i}s algebra for manifolds with conical singularities I}, year = {1994}, language = {en} } @article{SchroheSchulze1995, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Mellin quantization in the cone calculus for Boutet de Monvel{\"i}s algebra}, year = {1995}, language = {en} } @article{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Mellin and Green symbols for boundary value problems on manifolds with edges}, year = {1999}, language = {en} } @article{SchroheSchulze1998, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Mellin operators in a pseudodifferential calculus for boundary value problems on manifolds with edges}, year = {1998}, language = {en} } @article{SchroheSchulze1997, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {A symbol algebra for pseudodifferential boundary value problems on manifolds with edges}, year = {1997}, language = {en} } @book{SchroheSeiler2002, author = {Schrohe, Elmar and Seiler, J{\"o}rg}, title = {The resolvent of closed extensions of cone differential operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {28 S.}, year = {2002}, language = {en} } @unpublished{SchroheSeiler1999, author = {Schrohe, Elmar and Seiler, J{\"o}rg}, title = {Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25621}, year = {1999}, abstract = {Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces, it turns out to be independent of the choice of p. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators on Lp(B).}, language = {en} } @unpublished{SchroheSeiler2002, author = {Schrohe, Elmar and Seiler, J{\"o}rg}, title = {The resolvent of closed extensions of cone differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26378}, year = {2002}, abstract = {We study an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A )-¹ exists in a sector of the complex plane and decays like 1/|λ| as |λ| -> ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with striaght conical degeneracy and establish maximal regularity for the Cauchy problem u - Δu = f, u(0) = 0.}, language = {en} } @book{SchroheSeiler1999, author = {Schrohe, Elmar and Seiler, J{\"o}rg}, title = {Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {22 S.}, year = {1999}, language = {en} } @article{SchroeterSturmHolschneider2013, author = {Schr{\"o}ter, M-A and Sturm, H. and Holschneider, Matthias}, title = {Phase and amplitude patterns in DySEM mappings of vibrating microstructures}, series = {Nanotechnology}, volume = {24}, journal = {Nanotechnology}, number = {21}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0957-4484}, doi = {10.1088/0957-4484/24/21/215701}, pages = {10}, year = {2013}, abstract = {We use a dynamic scanning electron microscope (DySEM) to analyze the movement of oscillating micromechanical structures. A dynamic secondary electron (SE) signal is recorded and correlated to the oscillatory excitation of scanning force microscope (SFM) cantilever by means of lock-in amplifiers. We show, how the relative phase of the oscillations modulate the resulting real part and phase pictures of the DySEM mapping. This can be used to obtain information about the underlying oscillatory dynamics. We apply the theory to the case of a cantilever in oscillation, driven at different flexural and torsional resonance modes. This is an extension of a recent work (Schroter et al 2012 Nanotechnology 23 435501), where we reported on a general methodology to distinguish nonlinear features caused by the imaging process from those caused by cantilever motion.}, language = {en} } @unpublished{Schulze2003, author = {Schulze, Bert-Wolfgang}, title = {Crack theory with singularties at the boundary}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26600}, year = {2003}, abstract = {We investigate crack problems, where the crack boundary has conical singularities. Elliptic operators with two-sided elliptc boundary conditions on the plus and minus sides of the crack will be interpreted as elements of a corner algebra of boundary value problems. The corresponding operators will be completed by extra edge conditions on the crack boundary to Fredholm operators in corner Sobolev spaces with double weights, and there are parametrices within the calculus.}, language = {en} } @book{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {The structure of operators on manifolds with polyhedral singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {131 S.}, year = {2006}, language = {en} } @book{Schulze2008, author = {Schulze, Bert-Wolfgang}, title = {On a paper of Krupchyk, Tarkhanov and Tuomela}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {12 S.}, year = {2008}, language = {en} } @book{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential calculus on Manifolds with geometric singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {60 S.}, year = {2006}, language = {en} } @book{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Elliptic differential operators on Manifolds with Edges}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {14 S.}, year = {2006}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential calculus on manifolds with geometric singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30204}, year = {2006}, abstract = {Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development.}, language = {en} } @unpublished{Schulze2009, author = {Schulze, Bert-Wolfgang}, title = {Boundary value problems with the transmission property}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30377}, year = {2009}, abstract = {We give a survey on the calculus of (pseudo-differential) boundary value problems with the transmision property at the boundary, and ellipticity in the Shapiro-Lopatinskij sense. Apart from the original results of the work of Boutet de Monvel we present an approach based on the ideas of the edge calculus. In a final section we introduce symbols with the anti-transmission property.}, language = {en} } @unpublished{Schulze2008, author = {Schulze, Bert-Wolfgang}, title = {The iterative structure of corner operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30353}, year = {2008}, abstract = {We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference "Elliptic and Hyperbolic Equations on Singular Spaces", October 27 - 31, 2008, at the MSRI, University of Berkeley.}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Elliptic differential operators on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30188}, year = {2006}, abstract = {On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.}, language = {en} } @unpublished{Schulze2008, author = {Schulze, Bert-Wolfgang}, title = {On a paper of Krupchyk, Tarkhanov, and Tuomela}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30325}, year = {2008}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {The structure of operators on manifolds with polyhedral singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30099}, year = {2006}, abstract = {We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.}, language = {en} } @unpublished{Schulze2001, author = {Schulze, Bert-Wolfgang}, title = {Operators with symbol hierarchies and iterated asymptotics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25948}, year = {2001}, abstract = {Contents: Introduction 1 Edge calculus with parameters 1.1 Cone asymptotics and Green symbols 1.2 Mellin edge symbols 1.3 The edge symbol algebra 1.4 Operators on a manifold with edges 2 Corner symbols and iterated asymptotics 2.1 Holomorphic corner symbols 2.2 Meromorphic corner symbols and ellipicity 2.3 Weighted corner Sobolev spaces 2.4 Iterated asymptotics 3 The edge corner algebra with trace and potential conditions 3.1 Green corner operators 3.2 Smoothing Mellin corner operators 3.3 The edge corner algebra 3.4 Ellipicity and regularity with asymptotics 3.5 Examples and remarks}, language = {en} } @article{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {The trajectory attractor for a nonlinear elliptic system in a cylindrical domain with piecewise smooth boundary}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {37 S.}, year = {1999}, language = {en} } @book{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {31 S.}, year = {1999}, language = {en} } @book{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential calculus and applications to non-smooth configurations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {S. i - ii, 135 S.}, year = {1999}, language = {en} } @article{Schulze1995, author = {Schulze, Bert-Wolfgang}, title = {The variable discrete asymptotics in pseudo-differential boundary value problems II}, year = {1995}, language = {en} } @article{Schulze1997, author = {Schulze, Bert-Wolfgang}, title = {Boundary value problems and edges pseudo-differential operators}, year = {1997}, language = {en} } @article{Schulze1995, author = {Schulze, Bert-Wolfgang}, title = {The variable discrete asymptotics in pseudo-differential boundary value problems II}, year = {1995}, language = {en} } @article{Schulze1994, author = {Schulze, Bert-Wolfgang}, title = {The variable discrete asymptotics in pseudo-differential boundary value problems}, year = {1994}, language = {en} } @article{Schulze1994, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential operators, ellipticity and asymptotics on manifolds with edges}, year = {1994}, language = {en} } @article{Schulze1995, author = {Schulze, Bert-Wolfgang}, title = {Transmission algebras on singular spaces with components of different dimensions}, year = {1995}, language = {en} } @article{Schulze2001, author = {Schulze, Bert-Wolfgang}, title = {Operator algebras with symbol hierarchies on manifolds with singularities}, year = {2001}, language = {en} } @book{Schulze1994, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential boundary value problems, conical singularities, and asymptotics}, series = {Mathematical topics}, volume = {4}, journal = {Mathematical topics}, publisher = {Akad.-Verl.}, address = {Berlin}, isbn = {3-05-501597-5}, pages = {580 S.}, year = {1994}, language = {en} } @book{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Operator algebras with symbol hierarchies on manifolds with singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {31 S.}, year = {1999}, language = {en} } @article{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Iterated asymptotics on corner manifolds}, year = {1999}, language = {en} } @book{Schulze1998, author = {Schulze, Bert-Wolfgang}, title = {Differential equations on singular manifolds : semiclassical theory and operator algebras}, series = {Mathematical topics}, volume = {15}, journal = {Mathematical topics}, publisher = {Wiley-VCH}, address = {Berlin [u.a.]}, pages = {376 S.}, year = {1998}, language = {en} } @book{Schulze1998, author = {Schulze, Bert-Wolfgang}, title = {Boundary value problems and singular pseudo-differential operators}, publisher = {Wiley-VCH}, address = {Chichester [u.a.]}, pages = {XVI, 637 S.}, year = {1998}, language = {en} } @book{Schulze2003, author = {Schulze, Bert-Wolfgang}, title = {Toeplitz operators, and ellipticity of boundary value problems with global projection conditions}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {66 S.}, year = {2003}, language = {en} } @book{Schulze2003, author = {Schulze, Bert-Wolfgang}, title = {Crack theory with singularities at the boundary}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {36 S.}, year = {2003}, language = {en} } @book{Schulze2001, author = {Schulze, Bert-Wolfgang}, title = {Operators with symbol hierarchies and iterated asymptotics}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {53 S.}, year = {2001}, language = {en} } @article{Schulze2009, author = {Schulze, Bert-Wolfgang}, title = {On a paper of Krupchyk, Tarkhanov, and Tuomela}, issn = {0022-1236}, doi = {10.1016/j.jfa.2008.07.024}, year = {2009}, abstract = {We compare the above-mentioned article with the content of a previous publication}, language = {en} } @unpublished{Schulze2003, author = {Schulze, Bert-Wolfgang}, title = {Toeplitz operators, and ellipticity of boundary value problems with global projection conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26510}, year = {2003}, abstract = {Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.}, language = {en} } @unpublished{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Operator algebras with symbol hierarchies on manifolds with singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25647}, year = {1999}, abstract = {Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.}, language = {en} } @unpublished{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25596}, year = {1999}, abstract = {We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.}, language = {en} } @book{SchulzeDemuthAlbeverioetal.2001, author = {Schulze, Bert-Wolfgang and Demuth, Michael and Albeverio, Sergio and Schrohe, Elmar}, title = {Advances in Partial differential equations}, publisher = {Birkh{\"a}user}, address = {Basel}, year = {2001}, language = {en} } @unpublished{SchulzeNazaikinskiiSternin1999, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir E. and Sternin, Boris}, title = {On the homotopy classification of elliptic operators on manifolds with singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25574}, year = {1999}, abstract = {We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.}, language = {en} } @unpublished{SchulzeNazaikinskiiSternin1998, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris}, title = {The index of quantized contact transformations on manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25276}, year = {1998}, abstract = {The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.}, language = {en} } @unpublished{SchulzeNazaikinskiiSternin1998, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris}, title = {A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25296}, year = {1998}, abstract = {For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.}, language = {en} } @unpublished{SchulzeNazaikinskiiSterninetal.1997, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris and Shatalov, Victor}, title = {Spectral boundary value problems and elliptic equations on singular manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25147}, year = {1997}, abstract = {For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.}, language = {en} } @book{SchulzeNazajkinskijSternin1999, author = {Schulze, Bert-Wolfgang and Nazajkinskij, Vladimir E. and Sternin, Boris Ju.}, title = {On the homotopy classification of elliptic operators on manifolds with singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {22 S. : graph. Darst.}, year = {1999}, language = {en} } @book{SchulzeQin2005, author = {Schulze, Bert-Wolfgang and Qin, Yuming}, title = {Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {53 S.}, year = {2005}, language = {en} } @unpublished{SchulzeQin2005, author = {Schulze, Bert-Wolfgang and Qin, Yuming}, title = {Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29892}, year = {2005}, abstract = {In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.}, language = {en} } @unpublished{SchulzeSavinSternin1999, author = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris}, title = {Elliptic operators in subspaces and the eta invariant}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25496}, year = {1999}, abstract = {The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.}, language = {en} } @book{SchulzeSavinSternin1999, author = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris Ju.}, title = {The homotopy classification and the index of boundary value problems for general elliptic operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S. : graph. Darst.}, year = {1999}, language = {en} } @article{SchulzeSeiler2006, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Edge operators with conditions of Toeplitz type}, year = {2006}, abstract = {Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus}, language = {en} } @unpublished{SchulzeSeiler2001, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {The edge algebra structure of boundary value problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25955}, year = {2001}, abstract = {Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.}, language = {en} } @book{SchulzeSeiler2002, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Pseudodifferential boundary value problems with global projection conditions}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, pages = {37 S.}, year = {2002}, language = {en} } @book{SchulzeSeiler2002, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Edge operators with conditions of toeplitz type}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {20 S.}, year = {2002}, language = {en} } @book{SchulzeSeiler2001, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {The edge algebra structure of boundary value problems}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {52 S.}, year = {2001}, language = {en} } @article{SchulzeSeiler2004, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Boundary value problems with global projection conditions}, issn = {0022-1236}, year = {2004}, abstract = {Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved}, language = {en} } @article{SchulzeSeiler2019, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Elliptic complexes on manifolds with boundary}, series = {The journal of geometric analysis}, volume = {29}, journal = {The journal of geometric analysis}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-018-0014-6}, pages = {656 -- 706}, year = {2019}, abstract = {We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.}, language = {en} } @unpublished{SchulzeSeiler2002, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Pseudodifferential boundary value problems with global projection conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26233}, year = {2002}, abstract = {Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero}, language = {en} } @unpublished{SchulzeShlapunovTarkhanov1999, author = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Regularisation of mixed boundary problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25454}, year = {1999}, abstract = {We show an application of the spectral theorem in constructing approximate solutions of mixed boundary value problems for elliptic equations.}, language = {en} } @unpublished{SchulzeShlapunovTarkhanov2000, author = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Green integrals on manifolds with cracks}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25777}, year = {2000}, abstract = {We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.}, language = {en} } @book{SchulzeSlapunovTarchanov1999, author = {Schulze, Bert-Wolfgang and Slapunov, Aleksandr A. and Tarchanov, Nikolaj N.}, title = {Regularisation of mixed boundary problems}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {32 S.}, year = {1999}, language = {en} } @book{SchulzeSlapunovTarchanov2000, author = {Schulze, Bert-Wolfgang and Slapunov, Aleksandr A. and Tarchanov, Nikolaj N.}, title = {Green integrals on manifolds with cracks}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {33 S.}, year = {2000}, language = {en} } @article{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Nonstationary problems for Borel-Fuchs type equations}, year = {1997}, language = {en} } @article{SchulzeSterninSatalov1999, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On the index of elliptic operators on manifolds with conical singularities}, issn = {0002-3264}, year = {1999}, language = {en} } @article{SchulzeSterninSatalov1999, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On boundary value problems for elliptic equations}, issn = {0002-3264}, year = {1999}, language = {en} } @book{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On the index of differential operators on manifolds with conical singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 10}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {37 S.}, year = {1997}, language = {en} } @book{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Nonstationary problems for equations of Borel-Fuchs type}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 11}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {34 S.}, year = {1997}, language = {en} } @book{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On general boundary value problems for elliptic equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 35}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {36 S.}, year = {1997}, language = {en} } @article{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Structure rings of singularities and differential equations}, year = {1997}, language = {en} } @article{SchulzeSterninSatalov1997, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Operator algebras associated with resurgent transforms and differential equations on manifolds with singularities}, year = {1997}, language = {en} } @article{SchulzeSterninSatalov1994, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Resurgent analysis and differential equations with singularities}, year = {1994}, language = {en} } @article{SchulzeSterninSatalov1995, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Resurgent analysis in the theory of differential equations with singularities}, year = {1995}, language = {en} } @article{SchulzeSterninSatalov1998, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On general boundary value problems for elliptic equations}, issn = {0368-8666}, year = {1998}, language = {en} } @article{SchulzeSterninSatalov1998, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On the index of differential operators on manifolds with conical singularities}, year = {1998}, language = {en} }