Reverse Hardy-Littlewood-Sobolev inequalities
Analysis of PDEs
2019-09-17 v3
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 the properties of the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with free energy functionals and nonlinear diffusion equations involving mean field drifts.
Cite
@article{arxiv.1807.09189,
title = {Reverse Hardy-Littlewood-Sobolev inequalities},
author = {José A. Carrillo and Matías G. Delgadino and Jean Dolbeault and Rupert L. Frank and Franca Hoffmann},
journal= {arXiv preprint arXiv:1807.09189},
year = {2019}
}
Comments
This paper is based on the merging of arXiv:1803.06151 and arXiv:1803.06232