Attainability of the best Sobolev constant in a ball

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The best constant in the Sobolev inequality in the whole space is attained by the Aubin–Talenti function; however, this does not happen in bounded domains because of the break down of the dilation invariance. In this paper, we investigate a new scale invariant form of the Sobolev inequality in a ball and show that its best constant is attained by functions of the Aubin–Talenti type. Generalization to the Caffarelli–Kohn–Nirenberg inequality in a ball is also discussed.

Original languageEnglish
JournalMathematische Annalen
Volume375
Issue number1-2
DOIs
Publication statusPublished - 2019 Oct 8
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Attainability of the best Sobolev constant in a ball'. Together they form a unique fingerprint.

Cite this