Beyond Sobolev and Besov : regularity of solutions of PDEs and their traces in function spaces / Cornelia Schneider.

Author
Schneider, Cornelia (Mathematician) [Browse]
Format
Book
Language
English
Published/​Created
  • Cham, Switzerland : Springer, [2021]
  • ©2021
Description
xviii, 327 pages : illustrations (some color) ; 24 cm.

Availability

Copies in the Library

Location Call Number Status Location Service Notes
Lewis Library - Stacks QA323 .S36 2021 Browse related items Request

    Details

    Subject(s)
    Series
    • Lecture notes in mathematics (Springer-Verlag) ; 2291. [More in this series]
    • Lecture notes in mathematics, 0075-8434 ; volume 2291
    Summary note
    "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 Triebelizorkin 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."
    Bibliographic references
    Includes bibliographical references (pages 315-323) and index.
    Rights and reproductions note
    Current copyright fee: GBP19.00 42\0.
    Contents
    • Function Spaces and General Concepts
    • 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
    • Traces in Function Spaces
    • Traces on Lipschitz Domains
    • Traces of Generalized Smoothness Morrey Spaces on Domains
    • Traces on Riemannian Manifolds.
    Other title(s)
    Regularity of solutions of PDEs and their traces in function spaces
    ISBN
    • 9783030751388 ((paperback))
    • 3030751384 ((paperback))
    OCLC
    1259327286
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