Concentration Compactness: Functional-Analytic Theory of Concentration Phenomena

Cyril Tintarev

Published by De Gruyter 2020

Concentration Compactness

Functional-Analytic Theory of Concentration Phenomena

Cyril Tintarev

Volume 33 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110532432

Overview
Contents

About this book

Concentration compactness methods are applied to PDE's that lack compactness properties, typically due to the scaling invariance of the underlying problem. This monograph presents a systematic functional-analytic presentation of concentration mechanisms and is by far the most extensive and systematic collection of mathematical tools for analyzing the convergence of functional sequences via the mechanism of concentration.

A comprehensive monograph on the state of the art of concentration compactness techniques
Summary of the last ten years of research on the topic
An authoritative overview of many deep results in modern functional analysis

Author / Editor information

Cyril Tintarev, Technion - Israel Institute of Technology, Israel

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	IX
1. Profile decomposition: a structured defect of compactness Requires Authentication Unlicensed Licensed Download PDF	1
2. Delta-convergence and weak convergence Requires Authentication Unlicensed Licensed Download PDF	15
3. Cocompact embeddings with the rescaling group Requires Authentication Unlicensed Licensed Download PDF	29
4. Profile decomposition in Banach spaces Requires Authentication Unlicensed Licensed Download PDF	59
5. More cocompact embeddings Requires Authentication Unlicensed Licensed Download PDF	81
6. Profile decompositions on subsets Requires Authentication Unlicensed Licensed Download PDF	101
7. Global compactness on Riemannian manifolds Requires Authentication Unlicensed Licensed Download PDF	117
8. Functions of bounded variation. Sobolev spaces on fractals Requires Authentication Unlicensed Licensed Download PDF	159
9. Sample applications to variational problems Requires Authentication Unlicensed Licensed Download PDF	173
10. Appendix Requires Authentication Unlicensed Licensed Download PDF	191
Common notations Requires Authentication Unlicensed Licensed Download PDF	207
Bibliography Requires Authentication Unlicensed Licensed Download PDF	209
Index Requires Authentication Unlicensed Licensed Download PDF	215

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in mathematical analysis.
Pages
- Front matter: 11
- Main content: 216
Keywords: Funktionalanalysis; Kompaktheit; Nichtlineare elliptische Differentialgleichung; Nichtlineare Funktionalanalysis; Schwache Konvergenz

eBook

Published: February 10, 2020
ISBN: 9783110532432

Hardcover

Published: February 10, 2020
ISBN: 9783110530346