Reverse Hardy-Littlewood-Sobolev inequalities
Jos\'e A. Carrillo, Mat\'ias G. Delgadino, Jean Dolbeault, Rupert L., Frank, Franca Hoffmann
TL;DR
This paper introduces a new family of reverse Hardy-Littlewood-Sobolev inequalities with positive power law kernels, exploring parameter ranges, optimal functions, and open questions on concentration phenomena linked to free energy and nonlinear diffusion.
Contribution
It presents a novel class of inequalities and analyzes their properties, including the behavior of optimal functions and open problems related to concentration effects.
Findings
Characterization of admissible parameters for the inequalities
Analysis of properties of optimal functions
Discussion of open problems on concentration phenomena
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.
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