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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Chang-Shou Lin and Zhi-Qiang Wang
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1685-1691
MSC (2000): Primary 35B33; Secondary 46E35
Published electronically: January 16, 2004
Erratum: Proc. Amer. Math. Soc. (recently posted)
MathSciNet review: 2051129
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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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Additional Information

Chang-Shou Lin
Affiliation: Department of Mathematics, National Chung Cheng University, Chiayi, Taiwan

Zhi-Qiang Wang
Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07245-4
PII: S 0002-9939(04)07245-4
Keywords: Weighted Sobolev inequalities, Extremal functions, Exact symmetry
Received by editor(s): October 30, 2002
Published electronically: January 16, 2004
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2004 American Mathematical Society