Free Energies and the Reversed HLS Inequality
Analysis of PDEs
2018-03-19 v1
Abstract
We prove reversed Hardy-Littlewood-Sobolev inequalities by carefully studying the natural associated free energies with direct methods of calculus of variations. Tightness is obtained by a dyadic argument, which quantifies the relative strength of the entropy functional versus the interaction energy. The existence of optimizers is shown in the class of . With respect to their regularity, we study conditions for optimizers to be bounded functions. In a related model, we show the condensation phenomena, which suggests that optimizers are not in general regular.
Keywords
Cite
@article{arxiv.1803.06232,
title = {Free Energies and the Reversed HLS Inequality},
author = {J. A. Carrillo and M. G. Delgadino},
journal= {arXiv preprint arXiv:1803.06232},
year = {2018}
}