Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

Thomas Runst, Winfried Sickel

• Publisher: De Gruyter
• Year: 2011
• Print ISBN: 9783110151138
• eBook ISBN: 9783110812411
• Edition: 1
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

No detailed description available for "Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations".

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<q
• 5.4 Powers of f
• 5.5 Supplements
• 6 Applications to semilinear elliptic boundary problems
• 6.1 Introduction
• 6.2 The admissibility of spaces of Besov-Triebel-Lizorkin type
• 6.3 Nonlinear perturbations of linear invertible operators
• 6.4 Results of Landesman-Lazer type
• 6.5 Results of Kazdan-Warner type
• 6.6 Results of Ambrosetti-Prodi type
• Bibliography
• Index