Linear and Quasilinear Parabolic Problems: Volume II: Function Spaces

by Herbert Amann

Overview

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 shastic differential equations, for example.

Product Details

ISBN-13:	9783030117627
Publisher:	Springer International Publishing
Publication date:	04/17/2019
Series:	Monographs in Mathematics , #106
Edition description:	1st ed. 2019
Pages:	462
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

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.