Overview
- Follows the steps of Vol. I "Abstract Linear Theory"
- Features a clear and rigorous presentation style
- Fills a gap in literature
Part of the book series: Monographs in Mathematics (MMA, volume 106)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Linear and Quasilinear Parabolic Problems
Book Subtitle: Volume II: Function Spaces
Authors: Herbert Amann
Series Title: Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-11763-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-11762-7Published: 01 May 2019
eBook ISBN: 978-3-030-11763-4Published: 16 April 2019
Series ISSN: 1017-0480
Series E-ISSN: 2296-4886
Edition Number: 1
Number of Pages: XVI, 462
Topics: Functional Analysis