Pseudo Differential Operators On Manifolds With Singularities
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Pseudo Differential Operators On Manifolds With Singularities
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Author : B.-W. Schulze
language : en
Publisher: Elsevier
Release Date : 1991-10-17
Pseudo Differential Operators On Manifolds With Singularities written by B.-W. Schulze and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-10-17 with Mathematics categories.
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
Pseudo Differential Operators Singularities Applications
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Author : Iouri Egorov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Pseudo Differential Operators Singularities Applications written by Iouri Egorov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-Günzburg, 12–19 July 1992. The modern theory of elliptic boundary value problems in domains having conical or edge singularities on the boundary as well as the classical theory of elliptic boundary value problems and the original Kondratiev theory are presented. This material forms the foundation for the second part of the book which contains a new construction of pseudo-differential operators with symbols corresponding to the singularities of the boundary of different dimensions. This allows in particular to obtain complete asymptotic expansions of solutions near these singularities.
Algebras Of Pseudodifferential Operators Near Edge And Corner Singularities
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Author : Christoph Dorschfeldt
language : en
Publisher: Wiley-VCH
Release Date : 1998-09-16
Algebras Of Pseudodifferential Operators Near Edge And Corner Singularities written by Christoph Dorschfeldt and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-16 with Mathematics categories.
This research monograph deals with analysis on manifolds with singularities. More precisely, it presents pseudodifferential operators near edges and corners. In particular, it considers parameter-dependent edge operators and edge operators of Mellin type. The investigation of such operator families is necessary to construct operator algebras on manifolds with higher singularities. A self-contained exposition in Mellin techniques and pseudodifferential operators with operator-valued symbols is given. The algebra of parameter-dependent edge operators is constructed. Finally, Mellin operators near corner singularities are investigated. The focus is on elliptic theory. Elliptic operators on manifolds with edges are constructed as well as parametrices to elliptic elements. The equivalence of ellipticity and the Fredholm property is shown. Close to corner singularities, edge operators of Mellin type are defined, a pseudodifferential calculus is presented and parametrices are constructed. Asymptotics are treated using analytic functions and the concept of continuous asymptotic types.
Advances In Pseudo Differential Operators
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Author : Ryuichi Ashino
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Advances In Pseudo Differential Operators written by Ryuichi Ashino and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.
Elliptic Theory On Singular Manifolds
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Author : Vladimir E. Nazaikinskii
language : en
Publisher: CRC Press
Release Date : 2005-08-12
Elliptic Theory On Singular Manifolds written by Vladimir E. Nazaikinskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-12 with Mathematics categories.
The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints. Starting from an ele
Boundary Value Problems And Singular Pseudo Differential Operators
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Author : Bert-Wolfgang Schulze
language : en
Publisher: John Wiley & Sons
Release Date : 1998-02-04
Boundary Value Problems And Singular Pseudo Differential Operators written by Bert-Wolfgang Schulze and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-04 with Mathematics categories.
With this volume, Wolfgang Schulze presents a study of pseudo-differential operators on singular spaces, and also of developments of the concept of ellipticity in operator algebra.
Pseudo Differential Operators
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Author : Heinz O. Cordes
language : en
Publisher: Springer
Release Date : 2006-11-15
Pseudo Differential Operators written by Heinz O. Cordes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Elliptic Mixed Transmission And Singular Crack Problems
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Author : Gohar Harutyunyan
language : en
Publisher: European Mathematical Society
Release Date : 2007
Elliptic Mixed Transmission And Singular Crack Problems written by Gohar Harutyunyan and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Mixed, transmission, or crack problems belong to the analysis of boundary value problems on manifolds with singularities. The Zaremba problem with a jump between Dirichlet and Neumann conditions along an interface on the boundary is a classical example. The central theme of this book is to study mixed problems in standard Sobolev spaces as well as in weighted edge spaces where the interfaces are interpreted as edges. Parametrices and regularity of solutions are obtained within a systematic calculus of boundary value problems on manifolds with conical or edge singularities. This calculus allows singularities on the interface and homotopies between mixed and crack problems. Additional edge conditions are computed in terms of relative index results. In a detailed final chapter, the intuitive ideas of the approach are illustrated, and there is a discussion of future challenges. A special feature of the text is the inclusion of many worked-out examples which help the reader to appreciate the scope of the theory and to treat new cases of practical interest. This book is addressed to mathematicians and physicists interested in models with singularities, associated boundary value problems, and their solvability strategies based on pseudo-differential operators. The material is also useful for students in higher semesters and young researchers, as well as for experienced specialists working in analysis on manifolds with geometric singularities, the applications of index theory and spectral theory, operator algebras with symbolic structures, quantisation, and asymptotic analysis.
Pseudo Differential Boundary Value Problems Conical Singularities And Asymptotics
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Author : Bert-Wolfgang Schulze
language : en
Publisher: Wiley-VCH
Release Date : 1994-07-12
Pseudo Differential Boundary Value Problems Conical Singularities And Asymptotics written by Bert-Wolfgang Schulze and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-12 with Mathematics categories.
In the monograph, the theory of pseudo-differential boundary value problems under the aspect of a calculus for conical singularities is studied. Here the inner normal to the boundary is regarded as the model cone of a wedge with the boundary as edge. The transmission property in Boutet de Monvel's sense as well as the theory of Visik and Eskin are particular cases. The results of Visik and Eskin are considerably extended. The operators belong to an algebra that contains the parametrices of the elliptic elements. The ellipticity refers to the interior and the boundary symbols of highest orders. Boundary value problems are treated as particular edge problems in terms of a calculus of pseudodifferential operators with operator-valued symbols acting in the edge Sobolev spaces of the author. The theory contains the essential ideas for treating the more general case of pseudo-differential operators on manifolds with edges. This also belongs to the motivations of the approach. Similarly to Boutet de Monvel's theory, the corresponding algebra consists of matrices with the additional trace and potential operators. The concrete operator-valued symbols are presented both with discrete and continuous asymptotics. This corresponds to the nature of the elliptic regularity that is also proved for both variants of asymptotics. Essential ingredients are Mellin operator conventions and weighted Sobolev spaces with asymptotics. The theory applies to a wide range of classical transmission and mixed problems and gives a description of parametrices on an complete symbolic level.
Approaches To Singular Analysis
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Author : Juan B. Gil
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Approaches To Singular Analysis written by Juan B. Gil and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This collection presents various approaches to analytic problems that arise in the context of singular spaces. It contains articles offering introductions to various pseudodifferential calculi and discussions of relations between them, plus invited papers from mathematicians who have made significant contributions to this field