Reverse Hardy-Littlewood-Sobolev inequalities

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Date
2018
Publishing date
07-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01837888
Dewey
Analyse
Sujet
reverse Hardy-Littlewood-Sobolev inequalities
URI
https://basepub.dauphine.fr/handle/123456789/17954
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Author
Carillo, José A.
4553 Department of Mathematics [Imperial College London]
Delgadino, Matías
4553 Department of Mathematics [Imperial College London]
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rupert, Frank
6961 Mathematisches Institut [München] [LMU]
Hoffmann, Franca
241021 Department of Computing and Mathematical sciences
Type
Document de travail / Working paper
Item number of pages
30
Abstract (EN)
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.