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Article Dans Une Revue International Mathematics Research Notices Année : 2013

The Euclidean Onofri inequality in higher dimensions

Résumé

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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hal-00658665 , version 1 (10-01-2012)

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Manuel del Pino, Jean Dolbeault. The Euclidean Onofri inequality in higher dimensions. International Mathematics Research Notices, 2013, 15, pp.3600-3611. ⟨hal-00658665⟩
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