Attainability of the best Sobolev constant in a ball

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
ジャーナルMathematische Annalen
375
1-2
DOI
出版ステータスPublished - 2019 10 8

ASJC Scopus subject areas

  • Mathematics(all)

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