Profile decomposition for sequences of Borel measures

Abstract

We prove that, if dichotomy occurs when the concentration-compactness principle is used, the dichotomizing sequence can be choosen so that a nontrivial part of it concentrates. Iterating this argument leads to a profile decomposition for arbitrary sequences of bounded Borel measures. To illustrate our results we give an application to the structure of bouded sequences in the Sobolev space $W^{1,p}({\mathbb{R}}^N)$.

20 pages

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