Four proofs of cocompacness for Sobolev embeddings
Functional Analysis
2016-01-20 v1
Abstract
Cocompactness is a property of embeddings between two Banach spaces, similar to but weaker than compactness, defined relative to some non-compact group of bijective isometries. In presence of a cocompact embedding, bounded sequences (in the domain space) have subsequences that can be represented as a sum of a well-structured "bubble decomposition" (or defect of compactness) plus a remainder vanishing in the target space. This note is an exposition of different proofs of cocompactness for Sobolev-type embeddings, which employ methods of classical PDE, potential theory, and harmonic analysis.
Keywords
Cite
@article{arxiv.1601.04873,
title = {Four proofs of cocompacness for Sobolev embeddings},
author = {Cyril Tintarev},
journal= {arXiv preprint arXiv:1601.04873},
year = {2016}
}