Reverse Hardy-Littlewood-Sobolev inequalities
arXiv:1807.09189 · doi:10.1016/j.matpur.2019.09.001
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.
This paper is based on the merging of arXiv:1803.06151 and arXiv:1803.06232