Reverse Hardy-Littlewood-Sobolev inequalities

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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https://hal.archives-ouvertes.fr/hal-01837888
Contributor : Jean Dolbeault <>
Submitted on : Monday, August 12, 2019 - 1:49:09 PM
Last modification on : Wednesday, August 14, 2019 - 1:22:17 AM

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  • HAL Id : hal-01837888, version 2
  • ARXIV : 1807.09189

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José Carrillo, Matías Delgadino, Jean Dolbeault, Rupert Frank, Franca Hoffmann. Reverse Hardy-Littlewood-Sobolev inequalities. 2019. ⟨hal-01837888v2⟩

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