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# Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg

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## Chiba , Horiuchi : Radial symmetry and …

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

## Radial symmetry and its breaking in …

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 vertical bar gamma vertical bar is large enough.

## The Caffarelli-Kohn-Nirenberg type …

F. Catrina and Z.-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl. Math. 54 (2001), no. 2, 229–258.
http://projecteuclid.org/euclid.pja/1325264388

## Symmetry breaking in Caffarelli-Kohn-Nirenberg …

Symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities Jean Dolbeault ... For d≥ 2, radial symmetry can be proved when bis close to a+1 Theorem 2.

## On radial symmetry and its breaking …

https://www.jstage.jst.go.jp/article/mjiu/47/0/47_49/_article

## SYMMETRY BREAKING OF EXTREMAL …

... On radial symmetry and its breaking in the Caffarelli-Kohn ... Symmetry Breaking of Extremals for the Caffarelli-Kohn-Nirenberg Inequalities in a ...
http://www.worldscientific.com/doi/abs/10.1142/S0219199702000786

## Extremal functions for …

Extremal functions for Caffarelli—Kohn—Nirenberg and logarithmic Hardy ... On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type ...
https://www.cambridge.org/core/journals/proceedings-of-the-royal...

## On radial symmetry and its breaking …

On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 1