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

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

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 |γ| is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nire...

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Veröffentlicht in:Mathematical Journal of Ibaraki University 2015, Vol.47, pp.49-63
Hauptverfasser: Chiba, Naoki, Horiuchi, Toshio
Format: Artikel
Sprache:eng
Schlagworte:
Best constant
CKN-type inequality
Degenerate elliptic equation
Hardy-Sobolev inequality
Weighted Hardy inequality
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container_title Mathematical Journal of Ibaraki University
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creator Chiba, Naoki
Horiuchi, Toshio
description 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 |γ| is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with p = 1 and isoperimetric inequalities with weights.
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subjects Best constant
CKN-type inequality
Degenerate elliptic equation
Hardy-Sobolev inequality
Weighted Hardy inequality
title On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 1
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