Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities

Lin, Chang-Shou; Wang, Zhi-Qiang

doi:10.1090/S0002-9939-04-07245-4

Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities
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by Chang-Shou Lin and Zhi-Qiang Wang PDF

Proc. Amer. Math. Soc. 132 (2004), 1685-1691 Request permission

Erratum: Proc. Amer. Math. Soc. 132 (2004), 2183-2183.

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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