## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for $p=1$

#### 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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 4 (2016), 51-55.

Dates
First available in Project Euclid: 1 April 2016

https://projecteuclid.org/euclid.pja/1459516319

Digital Object Identifier
doi:10.3792/pjaa.92.51

Mathematical Reviews number (MathSciNet)
MR3482751

Zentralblatt MATH identifier
1345.26026

Subjects
Primary: 35J70: Degenerate elliptic equations
Secondary: 35J60: Nonlinear elliptic equations

#### Citation

Chiba, Naoki; Horiuchi, Toshio. Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for $p=1$. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 4, 51--55. doi:10.3792/pjaa.92.51. https://projecteuclid.org/euclid.pja/1459516319

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