Reverse Hardy-Littlewood-Sobolev inequalities
Analysis of PDEs
2018-03-20 v1
Abstract
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and characterize the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with nonlinear diffusion equations involving mean field drifts.
Cite
@article{arxiv.1803.06151,
title = {Reverse Hardy-Littlewood-Sobolev inequalities},
author = {Jean Dolbeault and Rupert Frank and Franca Hoffmann},
journal= {arXiv preprint arXiv:1803.06151},
year = {2018}
}