The Euclidean Onofri inequality in higher dimensions

Manuel Del Pino, Jean Dolbeault

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The classical Onofri inequality in the two-dimensional sphere assumes a natural form in the plane when transformed via stereographic projection. We establish an optimal version of a generalization of this inequality in the d-dimensional Euclidean space for any d≥2, by considering the endpoint of a family of optimal Gagliardo-Nirenberg interpolation inequalities. Unlike the two-dimensional case, this extension involves a rather unexpected Sobolev-Orlicz norm, as well as a probability measure no longer related to stereographic projection.

Original languageEnglish
Pages (from-to)3600-3611
Number of pages12
JournalInternational Mathematics Research Notices
Volume2013
Issue number15
DOIs
Publication statusPublished - 12 Aug 2013

ASJC Scopus subject areas

  • Mathematics(all)

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