Overview
- Gives a comprehensive treatment of the relations between complex function spaces, the regularity theory of PDEs and traces
- Includes many figures illustrating connections and basic ideas
- Provides a systematic and well-written treatment of problems
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2291)
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Table of contents (10 chapters)
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Front Matter
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Besov and Fractional Sobolev Regularity of PDEs
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Front Matter
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Traces in Function Spaces
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Front Matter
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Back Matter
Keywords
- Adaptive Algorithms
- Besov Spaces
- Elliptic Partial Differential Equations
- Embeddings
- Heat Equation
- Hyperbolic Partial Differential Equations
- Kondratiev Spaces
- Nonsmooth Domains
- Parabolic Partial Differential Equations
- Partial Differential Equations
- Polyhedral Cones
- Regularity Theory
- Smoothness Morrey Spaces
- Sobolev Spaces
- Traces
- Triebel-Lizorkin Spaces
About this book
This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs. It consists of three parts. Part I, the introduction, provides a quick guide to function spaces and the general concepts needed. Part II is the heart of the monograph and deals with the regularity of solutions in Besov and fractional Sobolev spaces. In particular, it studies regularity estimates of PDEs of elliptic, parabolic and hyperbolic type on non smooth domains. Linear as well as nonlinear equations are considered and special attention is paid to PDEs of parabolic type. For the classes of PDEs investigated a justification is given for the use of adaptive numerical schemes. Finally, the last part has a slightly different focus and is concerned with traces in several function spaces such as Besov– and Triebel–Lizorkin spaces, but also in quite general smoothness Morrey spaces.
The book is aimed at researchers and graduate students working in regularity theory of PDEs and function spaces, who are looking for a comprehensive treatment of the above listed topics.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Beyond Sobolev and Besov
Book Subtitle: Regularity of Solutions of PDEs and Their Traces in Function Spaces
Authors: Cornelia Schneider
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-75139-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-75138-8Published: 01 June 2021
eBook ISBN: 978-3-030-75139-5Published: 31 May 2021
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 330
Number of Illustrations: 14 b/w illustrations, 44 illustrations in colour
Topics: Functional Analysis, Numerical Analysis, Abstract Harmonic Analysis, Approximations and Expansions, Global Analysis and Analysis on Manifolds