1. Profile decomposition for sequences of Borel measures
- Author
-
Mariş, Mihai
- Subjects
Mathematics - Functional Analysis ,Mathematics - Analysis of PDEs ,Mathematics - Classical Analysis and ODEs ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Analysis of PDEs (math.AP) ,Functional Analysis (math.FA) - 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}(\R^N)$., Comment: 20 pages
- Published
- 2014
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