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April 2016 Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for $p=1$
Naoki Chiba, Toshio Horiuchi
Proc. Japan Acad. Ser. A Math. Sci. 92(4): 51-55 (April 2016). DOI: 10.3792/pjaa.92.51

Abstract

The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with $p=1$. We show that symmetry breaking of the best constants occurs provided that a parameter $|\gamma|$ is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with $p=1$ and the isoperimetric inequalities with weights.

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Naoki Chiba. Toshio Horiuchi. "Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for $p=1$." Proc. Japan Acad. Ser. A Math. Sci. 92 (4) 51 - 55, April 2016. https://doi.org/10.3792/pjaa.92.51

Information

Published: April 2016
First available in Project Euclid: 1 April 2016

zbMATH: 1345.26026
MathSciNet: MR3482751
Digital Object Identifier: 10.3792/pjaa.92.51

Subjects:
Primary: 35J70
Secondary: 35J60

Rights: Copyright © 2016 The Japan Academy

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Vol.92 • No. 4 • April 2016
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