The Euclidean Onofri inequality in higher dimensions
Analysis of PDEs
2012-12-06 v1
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.
Cite
@article{arxiv.1201.2162,
title = {The Euclidean Onofri inequality in higher dimensions},
author = {Manuel Del Pino and Jean Dolbeault},
journal= {arXiv preprint arXiv:1201.2162},
year = {2012}
}