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

• Chiba Naoki

  Ibaraki University

• Horiuchi Toshio

  Ibaraki University

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 |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.

Journal

• Mathematical Journal of Ibaraki University

  Mathematical Journal of Ibaraki University 47 (0), 49-63, 2015

  Department of Mathematics, Faculty of Science, Ibaraki University

Keywords

• CKN-type inequality
• Hardy-Sobolev inequality
• Weighted Hardy inequality
• Degenerate elliptic equation
• Best constant

Details

• CRID: 1390282680251663872
• NII Article ID: 130005100042
• NII Book ID: AA11169155
• DOI: 10.5036/mjiu.47.49
• ISSN: 18834353
• ISSN: 13433636
• Web Site: https://www.jstage.jst.go.jp/article/mjiu/47/0/47_49/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed