Sharp interpolation inequalities on the sphere : new methods and consequences
Analysis of PDEs
2012-12-06 v1
Abstract
These notes are devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension two and higher interpolate between Poincar\'e, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. We emphasize the connexion between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere. We shall address a series of related observations and give proofs based on symmetrization and the ultraspherical setting.
Cite
@article{arxiv.1210.1853,
title = {Sharp interpolation inequalities on the sphere : new methods and consequences},
author = {Jean Dolbeault and Maria J. Esteban and Michal Kowalczyk and Michael Loss},
journal= {arXiv preprint arXiv:1210.1853},
year = {2012}
}