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

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 [absolute value of ([gamma])] is large enough. In the argument we effectively employ equivalence betwee...

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Veröffentlicht in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2016-04, Vol.92A (NO. 4), p.51
Hauptverfasser: Chiba, Naoki, Horiuchi, Toshio
Format: Artikel
Sprache:eng
Schlagworte:
Inequalities (Mathematics)
Mathematical research
Symmetry
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Zusammenfassung: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 [absolute value of ([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. Key words: CKN-type inequality; symmetry break; weighted Hardy-Sobolev inequality; best constant.
ISSN:0386-2194
DOI:10.3792/pjaa.92.51