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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Beyond Sobolev and Besov - Regularity of Solutions of PDEs and Their Traces in Function Spaces (Paperback, 1st ed. 2021)
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Beyond Sobolev and Besov - Regularity of Solutions of PDEs and Their Traces in Function Spaces (Paperback, 1st ed. 2021)
Series: Lecture Notes in Mathematics, 2291
Expected to ship within 10 - 15 working days
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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.
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