Linear and Quasilinear Parabolic Problems

Volume II: Function Spaces

By:

Herbert Amann

Format:

Hardback

Series:

Monographs in Mathematics

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Description

This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.

Release date Australia

May 1st, 2019

Author

Herbert Amann

Series

Monographs in Mathematics

Pages

462

Edition

1st ed. 2019

Audience

Professional & Vocational

Illustrations

XVI, 462 p.

ISBN-13

9783030117627

Product ID

29011210

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