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Oxford University Press (OUP), International Mathematics Research Notices

DOI: 10.1093/imrn/rns119

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The Euclidean Onofri Inequality in Higher Dimensions

Journal article published in 2012 by Manuel Del Pino, Jean Dolbeault ORCID
This paper is available in a repository.
This paper is available in a repository.

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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.