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Linear and Quasilinear Parabolic Problems = Volume II: Function Spaces /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Linear and Quasilinear Parabolic Problems/ by Herbert Amann.
Reminder of title:	Volume II: Function Spaces /
Author:	Amann, Herbert.
Description:	XVI, 462 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-11763-4
ISBN:	9783030117634

Linear and Quasilinear Parabolic Problems = Volume II: Function Spaces /
Amann, Herbert.

Linear and Quasilinear Parabolic ProblemsVolume II: Function Spaces /[electronic resource] :by Herbert Amann. - 1st ed. 2019. - XVI, 462 p.online resource. - Monographs in Mathematics,1061017-0480 ;. - Monographs in Mathematics,105.

Restriction-Extension Pairs -- Sequence Spaces -- Anisotropy -- Classical Spaces -- Besov Spaces -- Intrinsic Norms, Slobodeckii and Hölder Spaces -- Bessel Potential Spaces -- Triebel-Lizorkin Spaces -- Point-Wise Multiplications -- Compactness -- Parameter-Dependent Spaces.

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.

ISBN: 9783030117634

Standard No.: 10.1007/978-3-030-11763-4doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Linear and Quasilinear Parabolic Problems = Volume II: Function Spaces /
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