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Tintarev, Kyril. Concentration Compactness: Functional-Analytic Theory of Concentration Phenomena / Cyril Tintarev. — 1 online resource (xii, 216 pages). — (De Gruyter Series in Nonlinear Analysis and Applications). — In English. — <URL:http://elib.fa.ru/ebsco/2376057.pdf>.Record create date: 2/29/2020 Subject: Functional analysis.; MATHEMATICS — Functional Analysis.; Functional analysis. Collections: EBSCO Allowed Actions: –
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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.
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Table of Contents
- Preface
- Contents
- 1. Profile decomposition: a structured defect of compactness
- 2. Delta-convergence and weak convergence
- 3. Cocompact embeddings with the rescaling group
- 4. Profile decomposition in Banach spaces
- 5. More cocompact embeddings
- 6. Profile decompositions on subsets
- 7. Global compactness on Riemannian manifolds
- 8. Functions of bounded variation. Sobolev spaces on fractals
- 9. Sample applications to variational problems
- 10. Appendix
- Common notations
- Bibliography
- Index
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