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

✍ Scribed by Thomas Runst

• Publisher: de Gruyter
• Year: 2011
• Tongue: English
• Leaves: 556
• Series: de Gruyter Nonlinear Analysis and Applications; 3
• Edition: Reprint
• Category: Library

✦ Synopsis

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Editor-in-Chief
Jürgen Appell, Würzburg, Germany

Honorary and Advisory Editors
Catherine Bandle, Basel, Switzerland
Alain Bensoussan, Richardson, Texas, USA
Avner Friedman, Columbus, Ohio, USA
Umberto Mosco, Worcester, Massachusetts, USA
Louis Nirenberg, New York, USA
Alfonso Vignoli, Rome, Italy

Editorial Board
Manuel del Pino, Bath, UK, and Santiago, Chile
Mikio Kato, Nagano, Japan
Wojciech Kryszewski, Toruń, Poland
Vicenţiu D. Rădulescu, Kraków, Poland
Simeon Reich, Haifa, Israel

Please submit book proposals to Jürgen Appell.

Titles in planning include

Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019)
Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019)
Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019)
Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020)
Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)
Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

✦ 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