Reverse Hardy-Littlewood-Sobolev inequalities

2018/03/16 by Dolbeault, Jean, Frank, Rupert, Hoffmann, Franca · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.06151

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 characterize the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with nonlinear diffusion equations involving mean field drifts.

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• Ground states and phase transitions for an aggregation model with fast diffusion on sphere
• An almost-almost-Schur lemma on the 3-sphere
• Generalized affine Hardy-Littlewood-Sobolev inequalities

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