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arXiv · 1408.4583

Defect of compactness in spaces of bounded variation

Adimurthi·Cyril Tintarev
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Abstract

Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. This paper extends the profile decomposition for Sobolev spaces proved by Solimini (AIHP 1995) to the non-reflexive case p=1. Since existence of concentration profiles relies on weak-star compactness, the corresponding result is set in a larger, conjugate, space of functions of bounded variation. We prove existence of minimizers for related inequalities and generalizations for to spaces of bounded variation on Lie groups.

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Adimurthi, Cyril Tintarev. 2014-08-20. Defect of compactness in spaces of bounded variation. https://arxiv.org/abs/1408.4583

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