Mihai Mariş
Published 2014-10-22Version 1
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)$.
The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order
On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Concentration analysis and cocompactness
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