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arXiv · 1201.2162

The Euclidean Onofri inequality in higher dimensions

Manuel Del Pino·Jean Dolbeault
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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\geq2, 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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Manuel Del Pino, Jean Dolbeault. 2012-01-10. The Euclidean Onofri inequality in higher dimensions. https://doi.org/10.1093/imrn%2Frns119

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