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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/4097298
Page Count: 7
You can always find the topics here!Topics: Mathematical inequalities, Mathematical functions, Symmetry, Mathematical constants, Elliptic equations, Hyperplanes, Inner products, Mathematical independent variables, Maximum principle, Cylinders
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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.
Proceedings of the American Mathematical Society © 2004 American Mathematical Society