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Reverse Hardy-Littlewood-Sobolev inequalities

Dolbeault, Jean and Frank, Rupert L. and Hoffmann, Franca (2018) Reverse Hardy-Littlewood-Sobolev inequalities. . (Submitted)

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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 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.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:© 2018 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. This research has been partially supported by the projects EFI, contract ANR-17-CE40-0030 (J.D.) and Kibord, contract ANR-13-BS01-0004 (J.D., F.H.) of the French National Research Agency (ANR), and by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.). The research stay of F.H. in Paris in December 2017 was partially supported by the Simons Foundation and by Mathematisches Forschungsinstitut Oberwolfach. Some of the preliminary investigations were done at the Institute Mittag-Leffler during the fall program Interactions between Partial Differential Equations & Functional Inequalities. The authors thank J.A. Carrillo for preliminary discussions which took place there and R.L.F. thanks the University Paris-Dauphine for hospitality in February 2018.
Funding AgencyGrant Number
Agence Nationale pour la Recherche (ANR)ANR-17-CE40-0030
Agence Nationale pour la Recherche (ANR)ANR-13-BS01-0004
Simons FoundationUNSPECIFIED
Mathematisches Forschungsinstitut OberwolfachUNSPECIFIED
Subject Keywords:Reverse Hardy-Littlewood-Sobolev inequalities; interpolation; non-linear diffusion; free energy; symmetrization; concentration; minimizer; existence of optimal functions; regularity; Euler–Lagrange equations
Classification Code:2010 Mathematics Subject Classification. Primary: 35A23; Secondary: 26D15, 35K55, 46E35, 49J40
Record Number:CaltechAUTHORS:20180604-111058055
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86785
Deposited By: Tony Diaz
Deposited On:04 Jun 2018 18:16
Last Modified:04 Jun 2018 18:16

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