Profile decomposition for sequences of Borel measures
Analysis of PDEs
2014-10-23 v1 Classical Analysis and ODEs
Functional Analysis
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 .
Cite
@article{arxiv.1410.6125,
title = {Profile decomposition for sequences of Borel measures},
author = {Mihai Mariş},
journal= {arXiv preprint arXiv:1410.6125},
year = {2014}
}
Comments
20 pages