Beyond Sobolev and Besov : Regularity of Solutions of PDEs and Their Traces in Function Spaces
Author(s)
Bibliographic Information
Beyond Sobolev and Besov : Regularity of Solutions of PDEs and Their Traces in Function Spaces
（Lecture notes in mathematics, 2291）
Springer, c2021
- : pbk
Available at / 30 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkL/N||LNM||2291200041793144
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: pbk/SCH 572080475416
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Note
Includes bibliographical references (p. 315-323) and index
Description and Table of Contents
Description
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.
Table of Contents
- Introduction. - Function Spaces and General Concepts. - Part I Besov and Fractional Sobolev Regularity of PDEs. - Theory and Background Material for PDEs. - Regularity Theory for Elliptic PDEs. - Regularity Theory for Parabolic PDEs. - Regularity Theory for Hyperbolic PDEs. - Applications to Adaptive Approximation Schemes. - Part II Traces in Function Spaces. - Traces on Lipschitz Domains. - Traces of Generalized Smoothness Morrey Spaces on Domains. - Traces on Riemannian Manifolds.
by "Nielsen BookData"
