Reverse Hardy-Littlewood-Sobolev inequalities

Jean Dolbeault, Rupert L. Frank & Franca Hoffmann
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 characterize the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with non-linear diffusion equations involving mean field drifts.
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