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arXiv · 1807.09189

Reverse Hardy-Littlewood-Sobolev inequalities

José A. Carrillo·Matías G. Delgadino·Jean Dolbeault·Rupert L. Frank·Franca Hoffmann
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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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José A. Carrillo, Matías G. Delgadino, Jean Dolbeault, Rupert L. Frank, Franca Hoffmann. 2018-07-20. Reverse Hardy-Littlewood-Sobolev inequalities. https://doi.org/10.1016/j.matpur.2019.09.001

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