@unpublished{Zehmisch2008,
  author    = {Zehmisch, Ren{\´e}},
  title     = {{\"U}ber Waldidentit{\"a}ten der Brownschen Bewegung},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49469},
  year      = {2008},
  abstract  = {Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einf{\"u}hrung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen {\"U}berschreitungszeit der Brown- schen Bewegung 2.9 Waldidentit{\"a}ten f{\"u}r die {\"U}berschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentit{\"a}t 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentit{\"a}t 3.4 St{\"a}rkere Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele f{\"u}r lokale Martingale f{\"u}r die Verfeinerung der ersten Waldidentit{\"a}t 3.7 {\"U}berschreitungszeiten der Brownschen Bewegung f{\"u}r nichtlineare Schranken 4 Zweite Waldidentit{\"a}t 4.1 Zweite Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 5 Dritte Waldidentit{\"a}t 5.1 Dritte Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentit{\"a}t 5.3 Eine wichtige Voraussetzung f{\"u}r die Verfeinerung der drittenWal- didentit{\"a}t 5.4 Verfeinerung der dritten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentit{\"a}ten im Mehrdimensionalen 6.1 Erste Waldidentit{\"a}t im Mehrdimensionalen 6.2 Zweite Waldidentit{\"a}t im Mehrdimensionalen 6.3 Dritte Waldidentit{\"a}t im Mehrdimensionalen 7 Appendix},
  language  = {de}
}
@unpublished{KytmanovMyslivetsTarkhanov2004,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Zeta-function of a nonlinear system},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26795},
  year      = {2004},
  abstract  = {Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.},
  language  = {en}
}
@unpublished{BaerPfaeffle2012,
  author    = {B{\"a}r, Christian and Pf{\"a}ffle, Frank},
  title     = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998},
  year      = {2012},
  abstract  = {This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schr{\"o}dinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.},
  language  = {en}
}
@unpublished{ManicciaMughetti2001,
  author    = {Maniccia, L. and Mughetti, M.},
  title     = {Weyl calculus for a class of subelliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26038},
  year      = {2001},
  abstract  = {Weyl-H{\"o}rmander calculus is used to get a parametrix in OPS¹-m sub(½, ½)(Ω)for a class of subelliptic pseudodifferential operators in OPS up(m)sub(1, 0)(Ω) with real non-negative principal symbol.},
  language  = {en}
}
@unpublished{BrauerKarp2008,
  author    = {Brauer, Uwe and Karp, Lavi},
  title     = {Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30347},
  year      = {2008},
  abstract  = {We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2015,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Weak boundary values of solutions of Lagrangian problems},
  volume    = {4},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617},
  pages     = {24},
  year      = {2015},
  abstract  = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.},
  language  = {en}
}
@unpublished{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231},
  year      = {1998},
  abstract  = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.},
  language  = {en}
}
@unpublished{LiuYangLu2002,
  author    = {Liu, Weian and Yang, Yin and Lu, Gang},
  title     = {Viscosity solutions of fully nonlinear parabolic systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26215},
  year      = {2002},
  abstract  = {In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].},
  language  = {en}
}
@unpublished{Alsaedy2016,
  author    = {Alsaedy, Ammar},
  title     = {Variational primitive of a differential form},
  volume    = {5},
  number    = {4},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89223},
  pages     = {8},
  year      = {2016},
  abstract  = {In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Unitary solutions of partial differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29852},
  year      = {2005},
  abstract  = {We give an explicit construction of a fundamental solution for an arbitrary non-degenerate partial differential equation with smooth coefficients.},
  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{Roelly2010,
  author    = {Roelly, Sylvie},
  title     = {Unas propiedades basicas de procesos de ramificaci{\´o}n : Lectures held at ICIMAF La Habana, Cuba, 2009 and 2010},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49620},
  year      = {2010},
  abstract  = {Aus dem Inhalt: 1. Unas propiedades de los procesos de Bienaym{\´e}-Galton-Watson de tiempo dis- creto (BGW) 2. Unas propiedades del proceso BGW de tiempo continuo 3. Limites de procesos de BGW cuando la poblaci{\´o}n es numerosa},
  language  = {mul}
}
@unpublished{KleinRosenberger2012,
  author    = {Klein, Markus and Rosenberger, Elke},
  title     = {Tunneling for a class of difference operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56989},
  year      = {2012},
  abstract  = {We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schr{\"o}dinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.},
  language  = {en}
}
@unpublished{GairingHoegeleKosenkova2016,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana},
  title     = {Transportation distances and noise sensitivity of multiplicative L{\´e}vy SDE with applications},
  volume    = {5},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86693},
  pages     = {24},
  year      = {2016},
  abstract  = {This article assesses the distance between the laws of stochastic differential equations with multiplicative L{\´e}vy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L{\´e}vy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.},
  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{Harutyunyan2001,
  author    = {Harutyunyan, Anahit V.},
  title     = {Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26110},
  year      = {2001},
  abstract  = {This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved.},
  language  = {en}
}
@unpublished{LouisRouquier2009,
  author    = {Louis, Pierre-Yves and Rouquier, Jean-Baptiste},
  title     = {Time-to-Coalescence for interacting particle systems : parallel versus sequential updating},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49454},
  year      = {2009},
  abstract  = {Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem with singular interfaces as a corner boundary value problem},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26855},
  year      = {2004},
  abstract  = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y , i.e., Au = f in int X, T±u = g± on int Y±, where Y is subdivided into subsets Y± with an interface Z and boundary conditions T± on Y± that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z ⊂ Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in [3]. With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z \ {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.},
  language  = {en}
}
@unpublished{DinesHarutjunjanSchulze2003,
  author    = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem in edge Sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26615},
  year      = {2003},
  abstract  = {Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.},
  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{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Riemann-Roch theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25051},
  year      = {1997},
  abstract  = {The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.},
  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}
}
@unpublished{Davis2003,
  author    = {Davis, Simon},
  title     = {The quantum cosmological wavefunction at very early times for a quadratic gravity theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26520},
  year      = {2003},
  abstract  = {The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.},
  language  = {en}
}
@unpublished{MartinSchulze2005,
  author    = {Martin, C.-I. and Schulze, Bert-Wolfgang},
  title     = {The quantisation of edge symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29959},
  year      = {2005},
  abstract  = {We investigate operators on manifolds with edges from the point of view of the symbolic calculus induced by the singularities. We discuss new aspects of the quantisation of edge-degenerate symbols which lead to continuous operators in weighted edge spaces.},
  language  = {en}
}
@unpublished{MeraTarkhanov2016,
  author    = {Mera, Azal and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Neumann problem after Spencer},
  volume    = {5},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-90631},
  pages     = {21},
  year      = {2016},
  abstract  = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.},
  language  = {en}
}
@unpublished{Tepoyan2008,
  author    = {Tepoyan, Liparit},
  title     = {The mixed problem for a degenerate operator equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30334},
  year      = {2008},
  abstract  = {We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2012,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {The method of Fischer-Riesz equations for elliptic boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61792},
  year      = {2012},
  abstract  = {We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.},
  language  = {en}
}
@unpublished{TarkhanovWallenta2012,
  author    = {Tarkhanov, Nikolai Nikolaevich and Wallenta, Daniel},
  title     = {The Lefschetz number of sequences of trace class curvature},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56969},
  year      = {2012},
  abstract  = {For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.},
  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{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{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of higher order operators on singular surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127},
  year      = {1998},
  abstract  = {The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1997,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of elliptic operators on manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096},
  year      = {1997},
  abstract  = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.},
  language  = {en}
}
@unpublished{BoeckmannSarkoezi1999,
  author    = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos},
  title     = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847},
  year      = {1999},
  abstract  = {The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.},
  language  = {en}
}
@unpublished{WenyiTianbo2005,
  author    = {Wenyi, Chen and Tianbo, Wang},
  title     = {The hypoellipticity of differential forms on closed manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29803},
  year      = {2005},
  abstract  = {In this paper we consider the hypo-ellipticity of differential forms on a closed manifold.The main results show that there are some topological obstruct for the existence of the differential forms with hypoellipticity.},
  language  = {de}
}
@unpublished{SchulzeSterninSavin1999,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Savin, Anton},
  title     = {The homotopy classification and the index of boundary value problems for general elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25568},
  year      = {1999},
  abstract  = {We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.},
  language  = {en}
}
@unpublished{PfaeffleStephan2012,
  author    = {Pf{\"a}ffle, Frank and Stephan, Christoph A.},
  title     = {The Holst action by the spectral action principle},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60032},
  year      = {2012},
  abstract  = {We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.},
  language  = {en}
}
@unpublished{Gilkey1998,
  author    = {Gilkey, Peter},
  title     = {The heat content asymptotics for variable geometries},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25381},
  year      = {1998},
  abstract  = {We study the heat content asymptotics on a compact manifold with boundary defened by a time dependent family of operators of Laplace type.},
  language  = {en}
}
@unpublished{Duduchava1999,
  author    = {Duduchava, Roland},
  title     = {The Green formula and layer potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25601},
  year      = {1999},
  abstract  = {The Green formula is proved for boundary value problems (BVPs), when "basic" operator is arbitrary partial differential operator with variable matrix coefficients and "boundary" operators are quasi-normal with vector-coeficients. If the system possesses the fundamental solution, representation formula for a solution is derived and boundedness properties of participating layer potentials from function spaces on the boundary (Besov, Zygmund spaces) into appropriate weighted function spaces on the inner and the outer domains are established. Some related problems are discussed in conclusion: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae,Calder{\´o}n projections, restricted smoothness of the underlying surface and coefficients. The results have essential applications in investigations of BVPs by the potential method, in apriori estimates and in asymptotics of solutions.},
  language  = {en}
}
@unpublished{CalinDerChen2004,
  author    = {Calin, Ovidium and Der-Chen, Chang},
  title     = {The geometry on a step 3 Grushin model},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26724},
  year      = {2004},
  abstract  = {In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.},
  language  = {en}
}
@unpublished{GlebovKiselev2005,
  author    = {Glebov, S. G. and Kiselev, O. M.},
  title     = {The forced KdV equation and passage through resonance},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29975},
  year      = {2005},
  abstract  = {We construct a special asymptotic solution for the forced KdV equation. In the frame of the shallow water model this kind of the external driving force is related to the atmospheric disturbance. The perturbation slowly passes through a resonance and it leads to the solution exchange. The detailed asymptotic description of the process is presented.},
  language  = {en}
}
@unpublished{MakhmudovTarkhanov2014,
  author    = {Makhmudov, Olimdjan and Tarkhanov, Nikolai Nikolaevich},
  title     = {The first mixed problem for the nonstationary Lam{\´e} system},
  volume    = {3},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71923},
  pages     = {19},
  year      = {2014},
  abstract  = {We find an adequate interpretation of the Lam{\´e} operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam{\´e} system.},
  language  = {en}
}
@unpublished{ChenLi2007,
  author    = {Chen, Hua and Li, Ke},
  title     = {The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30247},
  year      = {2007},
  abstract  = {Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.},
  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}
}
@unpublished{DebusscheHoegeleImkeller2013,
  author    = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter},
  title     = {The dynamics of nonlinear reaction-diffusion equations with small levy noise preface},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2085},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-00828-8; 978-3-319-00827-1},
  issn      = {0075-8434},
  pages     = {V -- +},
  year      = {2013},
  language  = {en}
}
@unpublished{DebusscheHoegeleImkeller2013,
  author    = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter},
  title     = {The dynamics of nonlinear reaction-diffusion equations with small levy noise},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2085},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-00828-8; 978-3-319-00827-1},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-00828-8_1},
  pages     = {1 -- 10},
  year      = {2013},
  abstract  = {Our primary interest in this book lies in the study of dynamical properties of reaction-diffusion equations perturbed by L{\´e}vy noise of intensity ? in the small noise limit ??0 .},
  language  = {en}
}
@unpublished{KrainerSchulze2004,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {The conormal symbolic structure of corner boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26662},
  year      = {2004},
  abstract  = {Ellipticity of operators on manifolds with conical singularities or parabolicity on space-time cylinders are known to be linked to parameter-dependent operators (conormal symbols) on a corresponding base manifold. We introduce the conormal symbolic structure for the case of corner manifolds, where the base itself is a manifold with edges and boundary. The specific nature of parameter-dependence requires a systematic approach in terms of meromorphic functions with values in edge-boundary value problems. We develop here a corresponding calculus, and we construct inverses of elliptic elements.},
  language  = {en}
}
@unpublished{MakhmudovNiyozovTarkhanov2006,
  author    = {Makhmudov, O. and Niyozov, I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {The cauchy problem of couple-stress elasticity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30078},
  year      = {2006},
  abstract  = {We study the Cauchy problem for the oscillation equation of the couple-stress theory of elasticity in a bounded domain in R3. Both the displacement and stress are given on a part S of the boundary of the domain. This problem is densely solvable while data of compact support in the interior of S fail to belong to the range of the problem. Hence the problem is ill-posed which makes the standard calculi of Fourier integral operators inapplicable. If S is real analytic the Cauchy-Kovalevskaya theorem applies to guarantee the existence of a local solution. We invoke the special structure of the oscillation equation to derive explicit conditions of global solvability and an approximation solution.},
  language  = {en}
}
@unpublished{MakhmudovNiyozov2005,
  author    = {Makhmudov, O. I. and Niyozov, I. E.},
  title     = {The Cauchy problem for the Lame system in infinite domains in R up(m)},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29967},
  year      = {2005},
  abstract  = {We consider the problem of analytic continuation of the solution of the multidimensional Lame system in infinite domains through known values of the solution and the corresponding strain tensor on a part of the boundary, i.e,the Cauchy problem.},
  language  = {en}
}
@unpublished{LyTarkhanov2007,
  author    = {Ly, I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {The cauchy problem for nonlinear elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30228},
  year      = {2007},
  abstract  = {This paper is devoted to investigation of the Cauchy problem for nonlinear elliptic equations with a small parameter.},
  language  = {en}
}
@unpublished{KiselevTarkhanov2013,
  author    = {Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {The capture of a particle into resonance at potential hole with dissipative perturbation},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64725},
  year      = {2013},
  abstract  = {We study the capture of a particle into resonance at a potential hole with dissipative perturbation and periodic outside force. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.},
  language  = {en}
}