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Field name	Details
Dewey Class	515.353
Title	Beyond Sobolev and Besov ([EBook]) : regularity of solutions of PDEs and their traces in function spaces / Cornelia Schneider
Author	Schneider, Cornelia
Publication	Cham : Springer International Publishing , 2021
Physical Details	: online resource (xviii, 327 p.)
Series	Lecture notes in physics ; 2291
ISBN	978-3-030-75139-5
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 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.:
Mode of acces to digital resource	Digital reproduction.- Cham : Springer International Publishing, 2021. - Digital book. Cham Springer Nature 2021. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-75139-5
Links to Related Works	Subject References: Approximation theory . Approximations and Expansions . Functional Analysis . Harmonic analysis . Manifolds . Numerical Analysis . Authors: Schneider, Cornelia . Series: Lecture notes in physics . Classification: 515.353 . 515.353 (DDC 23) .

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Beyond Sobolev and Besov: regularity of solutions of PDEs and their traces in function spaces

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