@article{HarutjunjanSchulze2004, author = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang}, title = {Reduction of orders in boundary value problems without transmission property}, issn = {0025-5645}, year = {2004}, abstract = {Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We employ specific smooth symbols of arbitrary real orders and with parameters, and we show that the associated operators induce isomorphisms between Sobolev spaces on a given manifold with boundary. Such operators for integer orders have the transmission property and belong to the calculus of Boutet de Monvel [1], cf. also [9]. In general, they fit to the algebra of boundary value problems without the transmission property in the sense of [17] and [24]. Order reducing elements of the present kind are useful for constructing parametrices of mixed elliptic problems. We show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We then investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary. We finally construct order reducing operators on a compact manifold with conical singularities and boundary}, language = {en} } @article{RabinovichSchulzeTarkhanov2004, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Boundary value problems in oscillating cuspidal wedges}, issn = {0035-7596}, year = {2004}, abstract = {The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges}, 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} } @book{JaianiSchulze2004, author = {Jaiani, George V. and Schulze, Bert-Wolfgang}, title = {Some degenerate elliptic systems and applications to cousped plates}, 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 = {2004}, language = {en} } @book{HarutjunjanSchulze2004, author = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang}, title = {The zaremba problem with singular interfaces as a corner boundary value problem}, 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 = {48 S.}, year = {2004}, language = {en} } @book{SchulzeVolpato2004, author = {Schulze, Bert-Wolfgang and Volpato, A.}, title = {Green operators in the edge 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 = {24 S.}, year = {2004}, language = {en} } @book{EgorovKondratievSchulze2004, author = {Egorov, Yu. and Kondratiev, V. A. and Schulze, Bert-Wolfgang}, title = {On the completeness of root functions of elliptic boundary problems in a domain with conical points on 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 = {21 S.}, year = {2004}, language = {en} } @book{NazajkinskijSavinSchulzeetal.2004, author = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {On the homotopy classification of elliptic 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 = {26 S.}, year = {2004}, language = {en} } @book{LiuSchulze2004, author = {Liu, Xiaochun and Schulze, Bert-Wolfgang}, title = {Boundary value problems in edge representation}, 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 = {43 S.}, year = {2004}, language = {en} } @book{NazajkinskijSavinSchulzeetal.2004, author = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Elliptic theory 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 = {48 S.}, year = {2004}, language = {en} } @book{HarutjunjanSchulze2004, author = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang}, title = {Boundary problems with meromorphic symbols in cylindrical domains}, 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 = {19 S.}, year = {2004}, language = {en} } @book{CalvoMartinSchulze2004, author = {Calvo, D. and Martin, Calin-Iulian and Schulze, Bert-Wolfgang}, title = {Symbolic Structures on Corner Manifolds}, 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 = {18 S.}, year = {2004}, language = {en} } @book{KapanadzeSchulze2004, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact Problems for Domains with Conical 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 = {37 S.}, year = {2004}, language = {en} } @book{LiuSchulze2004, author = {Liu, Xiaochun and Schulze, Bert-Wolfgang}, title = {Ellipticity on Manifolds with edges and 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 = {35 S.}, year = {2004}, language = {en} } @book{NazajkinskijSavinSchulzeetal.2004, author = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {The index problem 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 = {27 S.}, year = {2004}, language = {en} } @book{KrainerSchulze2004, author = {Krainer, Thomas and Schulze, Bert-Wolfgang}, title = {The Conormal symbolic structure of corner 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 = {47 S.}, year = {2004}, language = {en} } @article{LiuSchulze2005, author = {Liu, Xiaochun and Schulze, Bert-Wolfgang}, title = {Ellipticity on manifolds with edges and boundary}, issn = {0026-9255}, year = {2005}, abstract = {Ellipticity of a manifold with edges and boundary is connected to boundary and edge conditions that complete corresponding operators to Fredholm operators between weighted Sobolev spaces. We study a new parameter-dependent calculus of elliptic operators, where the interior symbols have specific properties on the boundary. We construct elliptic operators with a prescribed number of edge conditions and obtain isomorphisms in the scale of edge Sobolev spaces}, language = {en} } @article{KytmanovMyslivetsSchulzeetal.2005, author = {Kytmanov, Alexander M. and Myslivets, Simona and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Elliptic problems for the Dolbeault complex}, issn = {0025-584X}, year = {2005}, abstract = {The inhomogeneous partial derivative-equation is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the analysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C-n. (C) 2005 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim}, language = {en} } @article{KapanadzeSchulze2005, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact problems for domains with conical singularities}, issn = {0022-0396}, year = {2005}, abstract = {We study boundary-contact problems for elliptic equations (and systems) with interfaces that have conical singularities. Such problems represent continuous operators between weighted Sobolev spaces and subspaces with asymptotics. Ellipticity is formulated in terms of extra transmission conditions along the interfaces with a control of the conormal symbolic structure near conical singularities. We show regularity and asymptotics of solutions in weighted spaces, and we construct parametrices. The result will be illustrated by a number of explicit examples. (c) 2004 Elsevier Inc. All rights reserved}, language = {en} } @article{HarutjunjanSchulze2005, author = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang}, title = {Boundary problems with meromorphic symbols in cylindrical domains}, issn = {0170-4214}, year = {2005}, abstract = {We show relative index formulas for boundary value problems in cylindrical domains and Sobolev spaces with different weights at too. The amplitude functions are meromorphic in the axial covariable and take values in the space of boundary value problems on the cross section of the cylinder. Copyright (c) 2005 John Wiley \& Sons, Ltd}, language = {en} }