Reverse Hardy-Littlewood-Sobolev inequalities

被引：13
|
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
收藏
页码：133 / 165
页数：33
相关论文
共 50 条
  • [41] On Nonlocal Choquard System with Hardy-Littlewood-Sobolev Critical Exponents
    Luo, Xiaorong
    Mao, Anmin
    Mo, Shuai
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2022, 32 (08)
  • [42] Sharp reversed Hardy-Littlewood-Sobolev inequality on R n
    Quoc Anh Ngo
    Van Hoang Nguyen
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 2017, 220 (01) : 189 - 223
  • [43] EXISTENCE TO FRACTIONAL CRITICAL EQUATION WITH HARDY-LITTLEWOOD-SOBOLEV NONLINEARITIES
    Nyamoradi, Nemat
    Razani, Abdolrahman
    [J]. ACTA MATHEMATICA SCIENTIA, 2021, 41 (04) : 1321 - 1332
  • [44] THE REVERSED HARDY-LITTLEWOOD-SOBOLEV TYPE INTEGRAL SYSTEMS WITH WEIGHTS
    Liu, Xiaoqian
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2019, 22 (03): : 989 - 996
  • [45] EXISTENCE TO FRACTIONAL CRITICAL EQUATION WITH HARDY-LITTLEWOOD-SOBOLEV NONLINEARITIES
    Nemat NYAMORADI
    Abdolrahman RAZANI
    [J]. Acta Mathematica Scientia, 2021, 41 (04) : 1321 - 1332
  • [46] Achievability of a supremum for the Hardy-Littlewood-Sobolev inequality with supercritical exponent
    An, Xiaoming
    Peng, Shuangjie
    Xie, Chaodong
    [J]. SCIENCE CHINA-MATHEMATICS, 2019, 62 (12) : 2497 - 2504
  • [47] Achievability of a supremum for the Hardy-Littlewood-Sobolev inequality with supercritical exponent
    Xiaoming An
    Shuangjie Peng
    Chaodong Xie
    [J]. Science China Mathematics, 2019, 62 : 2497 - 2504
  • [48] EXISTENCE OF THE MAXIMIZING PAIR FOR THE DISCRETE HARDY-LITTLEWOOD-SOBOLEV INEQUALITY
    Huang, Genggeng
    Li, Congming
    Yin, Ximing
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (03): : 935 - 942
  • [49] Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity
    Giacomoni, J.
    Mukherjee, T.
    Sreenadh, K.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 467 (01) : 638 - 672
  • [50] Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality
    WU Di
    SHI ZuoShunHua
    YAN DunYan
    [J]. Science China Mathematics, 2014, 57 (05) : 963 - 970
12345