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Symmetry of Extremal Functions for the Caffarelli-Kohn-Nirenberg Inequalities

Chang-Shou Lin and Zhi-Qiang Wang
Proceedings of the American Mathematical Society
Vol. 132, No. 6 (Jun., 2004), pp. 1685-1691
Stable URL: http://www.jstor.org/stable/4097298
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Symmetry of Extremal Functions for the Caffarelli-Kohn-Nirenberg Inequalities
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Abstract

We study the symmetry property of extremal functions to a family of weighted Sobolev inequalities due to Caffarelli-Kohn-Nirenberg. By using the moving plane method, we prove that all non-radial extremal functions are axially symmetric with respect to a line passing through the origin.

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