Authors:
- Presents the notion of ellipticity with an unification of Shapiro-Lopatinskij elliptic and global projection boundary conditions
- Discusses spectral boundary conditions for elliptic differential operators
- Describes Toeplitz-type operators on manifolds with edge, including operators with/without transmission property
Part of the book series: Operator Theory: Advances and Applications (OT, volume 265)
Part of the book sub series: Advances in Partial Differential Equations (APDE)
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Table of contents (13 chapters)
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Front Matter
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Boundary Value Problems with Global Projection Conditions
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Front Matter
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Edge Operators with Global Projection Conditions
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Front Matter
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BVPs without the Transmission Property
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Front Matter
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Back Matter
About this book
This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel’s calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.
Reviews
“The present book is devoted to developing general concepts of ellipticity of boundary value problems (BVPs) and provides a self-contained resource for use by professional researchers.” (David Kapanadze, zbMATH 1423.35003, 2019)
Authors and Affiliations
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School of Mathematics and Statistics, Wuhan University, Wuhan, China
Xiaochun Liu
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Institut für Mathematik, Universität Potsdam , Potsdam, Germany
Bert-Wolfgang Schulze
Bibliographic Information
Book Title: Boundary Value Problems with Global Projection Conditions
Authors: Xiaochun Liu, Bert-Wolfgang Schulze
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-319-70114-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-70113-4Published: 08 November 2018
Softcover ISBN: 978-3-030-09933-6Published: 15 December 2018
eBook ISBN: 978-3-319-70114-1Published: 30 October 2018
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XVI, 410
Topics: Partial Differential Equations, Global Analysis and Analysis on Manifolds, Operator Theory