Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the singularity on the boundary

Jann Long Chern, Chang Shou Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)

Abstract

Let Ω be a bounded smooth domain in RN, N ≧ 3 and Da1,2(Ω) be the completion of C0(Ω) with respect to the norm, The Caffarelli-Kohn-Nirenberg inequalities state that there is a constant C > 0 such that, We prove the best constant for (0.1), is always achieved in Da1,2(Ω)} provided that 0 ∈ ∂Ω and the mean curvature H(0) < 0, where a, b satisfies If a = 0 and 1 > b > 0, then the result was proved by Ghoussoub and Robert [12].

Original languageEnglish
Pages (from-to)401-432
Number of pages32
JournalArchive for Rational Mechanics and Analysis
Volume197
Issue number2
DOIs
Publication statusPublished - 2010
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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