Reverse Hardy-Littlewood-Sobolev inequalities

被引：16

作者：

Carrillo, Jose A. ^{[1
]}

Delgadino, Matias G. ^{[1
]}

Dolbeault, Jean ^{[2
]}

Frank, Rupert L. ^{[3
,4
]}

Hoffmann, Franca ^{[5
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Univ Paris 09, PSL Res Univ, Ctr Rech Math Decis, CNRS,UMR 7534, Pl Lattre de Tassigny, F-75775 Paris 16, France

[3] Ludwig Maximilians Univ Munchen, Math Inst, Theresienstr 39, D-80333 Munich, Germany

[4] CALTECH, Dept Math, Pasadena, CA 91125 USA

[5] CALTECH, Dept Comp & Math Sci, 1200 E Calif Blvd MC 305-16, Pasadena, CA 91125 USA

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 132卷

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

Reverse Hardy-Littlewood-Sobolev inequalities; Concentration; Regularity; Free energy; Nonlinear diffusion; Mean field equations; SHARP CONSTANTS; FUNCTIONALS; DIFFUSION; SPACE; MASS;

D O I：

10.1016/j.matpur.2019.09.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. Crown Copyright (C) 2019 Published by Elsevier Masson SAS. All rights reserved.

引用

页码：133 / 165

页数：33

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