Abstract
We are concerned with the best exponent in Concentration-Compactness principles for the borderline case of the Sobolev inequality. We present a new approach, which both yields a rigorous proof of the relevant principle in the standard case when functions vanishing on the boundary are considered, and enables us to deal with functions with unrestricted boundary values.
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This research was partly supported by the research project MSM 0021620839 of the Czech Ministry MŠMT, by the research project of MIUR (Italian Ministry of University) “Geometric aspects of partial differential equations and related optics”, and by the RSJ algorithmic trading grant.
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Černý, R., Cianchi, A. & Hencl, S. Concentration-compactness principles for Moser–Trudinger inequalities: new results and proofs. Annali di Matematica 192, 225–243 (2013). https://doi.org/10.1007/s10231-011-0220-3
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DOI: https://doi.org/10.1007/s10231-011-0220-3
Keywords
- Sobolev spaces
- Sharp constants
- Moser–Trudinger inequality
- Concentration-Compactness Principle
- Rearrangements
- Isoperimetric inequalities