Extremal functions for the Caffarelli-Kohn-Nirenberg inequalities: A simple proof of the symmetry

Bouchez, Vincent;Willem, Michel
(2009) Journal of Mathematical Analysis and Applications — Vol. 352, n° 1, p. 293-300 (2009)

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  • Bouchez, VincentUCLouvain
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  • Willem, MichelUCLouvain
    Author
Abstract
In this article, we give a simple proof of the result due to Lin and Wang ensuring the foliated Schwarz symmetry of the extremal functions for the Caffarelli-Kohn-Nirenberg inequalities. This new proof uses a direct and powerful method due to Bartsch, Weth and Willem using polarizations. (C) 2008 Elsevier Inc. All rights reserved.
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Bouchez, V., & Willem, M. (2009). Extremal functions for the Caffarelli-Kohn-Nirenberg inequalities: A simple proof of the symmetry. Journal of Mathematical Analysis and Applications, 352(1), 293-300. https://doi.org/10.1016/j.jmaa.2008.04.059 (Original work published 2009)