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Carrillo, Jose A.; Delgadino, Matias G.; Dolbeault, Jean; Frank, Rupert L. and Hoffmann, Franca (2019): Reverse Hardy-Littlewood-Sobolev inequalities. In: Journal De Mathematiques Pures et Appliquees, Vol. 132: pp. 133-165

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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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