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arXiv · 1601.04873

Four proofs of cocompacness for Sobolev embeddings

Cyril Tintarev
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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.

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Cyril Tintarev. 2016-01-19. Four proofs of cocompacness for Sobolev embeddings. https://arxiv.org/abs/1601.04873

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