Attainability of the best Sobolev constant in a ball

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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
Issue number1-2
Publication statusPublished - 2019 Oct 8
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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