Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations [Reprint ed.] 3110151138, 9783110151138
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English Pages 560 [556] Year 2011
Table of contents :
1 Introduction
2 Function spaces of Besov-Triebel-Lizorkin type
2.1 Definitions and fundamental properties
2.2 Embeddings
2.3 Some equivalent characterizations of Fsp,qand Bsp,q
2.4 Spaces on domains
2.5 Interpolation
2.6 Homogeneous spaces and a further supplement
3 Regular elliptic boundary value problems
3.1 Definitions and preliminaries
3.2 Estimates of integral operators
3.3 Estimates of the Poisson integral
3.4 A priori estimates
3.5 Regular elliptic boundary value problems
4 Pointwise multiplication
4.1 Introduction
4.2 The definition of the product
4.3 Necessary conditions for pointwise multiplication
4.4 Products of a function and a distribution
4.5 Products of functions and a distribution. The general case
4.6 The case of constant p
4.7 The extremal case p1 = p and p2 = .
4.8 Generalized Holder inequalities
4.9 The spaces Asp,q,unif and relations to M(Asp,q)
5 Nemytskij operators in spaces of Besov-Triebel-Lizorkin type
5.1 Introduction
5.2 Nemytskij operators in Lebesgue and Sobolev spaces
5.3 The Composition operator corresponding to a C.-function G in and Bsp
1 Introduction
2 Function spaces of Besov-Triebel-Lizorkin type
2.1 Definitions and fundamental properties
2.2 Embeddings
2.3 Some equivalent characterizations of Fsp,qand Bsp,q
2.4 Spaces on domains
2.5 Interpolation
2.6 Homogeneous spaces and a further supplement
3 Regular elliptic boundary value problems
3.1 Definitions and preliminaries
3.2 Estimates of integral operators
3.3 Estimates of the Poisson integral
3.4 A priori estimates
3.5 Regular elliptic boundary value problems
4 Pointwise multiplication
4.1 Introduction
4.2 The definition of the product
4.3 Necessary conditions for pointwise multiplication
4.4 Products of a function and a distribution
4.5 Products of functions and a distribution. The general case
4.6 The case of constant p
4.7 The extremal case p1 = p and p2 = .
4.8 Generalized Holder inequalities
4.9 The spaces Asp,q,unif and relations to M(Asp,q)
5 Nemytskij operators in spaces of Besov-Triebel-Lizorkin type
5.1 Introduction
5.2 Nemytskij operators in Lebesgue and Sobolev spaces
5.3 The Composition operator corresponding to a C.-function G in and Bsp
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