The Euclidean Onofri inequality in higher dimensions

Manuel Del Pino; Jean Dolbeault

doi:10.1093/imrn/rns119

The Euclidean Onofri inequality in higher dimensions

Manuel Del Pino, Jean Dolbeault

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Citations (SciVal)

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 language	English
Pages (from-to)	3600-3611
Number of pages	12
Journal	International Mathematics Research Notices
Volume	2013
Issue number	15
DOIs	https://doi.org/10.1093/imrn/rns119
Publication status	Published - 12 Aug 2013

Funding

This research was supported by the projects CBDif and EVOL of the French National Research

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rns119

Cite this

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AB - 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.

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The Euclidean Onofri inequality in higher dimensions

Abstract

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