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Linear and quasilinear parabolic pro...

Amann, Herbert.

Linear and quasilinear parabolic problems.Volume II,Function spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Linear and quasilinear parabolic problems.by Herbert Amann.
remainder title:	Function spaces
Author:	Amann, Herbert.
Published:	Cham :Springer International Publishing :2019.
Description:	xvi, 462 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equations, Parabolic.
Online resource:	https://doi.org/10.1007/978-3-030-11763-4
ISBN:	9783030117634$q(electronic bk.)

Linear and quasilinear parabolic problems.Volume II,Function spaces
Amann, Herbert.

Linear and quasilinear parabolic problems.Volume II,Function spaces[electronic resource] /Function spacesby Herbert Amann. - Cham :Springer International Publishing :2019. - xvi, 462 p. :ill., digital ;24 cm. - Monographs in mathematics,v.1061017-0480 ;. - Monographs in mathematics ;v.102..

Restriction-Extension Pairs -- Sequence Spaces -- Anisotropy -- Classical Spaces -- Besov Spaces -- Intrinsic Norms, Slobodeckii and Holder 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 Holder 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$q(electronic bk.)

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

247280
Differential equations, Parabolic.

LC Class. No.: QA377 / .A43 2019

Dewey Class. No.: 515.3534

Linear and quasilinear parabolic problems.Volume II,Function spaces
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505 0 $a Restriction-Extension Pairs -- Sequence Spaces -- Anisotropy -- Classical Spaces -- Besov Spaces -- Intrinsic Norms, Slobodeckii and Holder Spaces -- Bessel Potential Spaces -- Triebel-Lizorkin Spaces -- Point-Wise Multiplications -- Compactness -- Parameter-Dependent Spaces.
520 $a 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 Holder 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.
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