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Detailed view Article in peer-reviewed journal
International Mathematics Research Notices (2012) 10.1093/imrn/rns119
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The Euclidean Onofri inequality in higher dimensions
Manuel Del Pino1, Jean Dolbeault2

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.
1:  DIM - Departamento de Ingeniería Matemática [Santiago]
2:  CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
Sobolev inequality – logarithmic Sobolev inequality – Onofri inequalities – Gagliardo-Nirenberg inequalities – interpolation – extremal functions – optimal constants – stereographic projection