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Reverse Hardy-Littlewood-Sobolev inequalities

Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca (2018), Reverse Hardy-Littlewood-Sobolev inequalities. https://basepub.dauphine.fr/handle/123456789/17955

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01735446
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
19
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Author(s)
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Frank, Rupert L.
Mathematisches Institut [München] [LMU]
Department of Mathematics (Caltech)
Hoffmann, Franca
Mathematisches Institut [München] [LMU]
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 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.
Subjects / Keywords
Euler--Lagrange equations; regularity; symmetrization; free energy; existence of optimal functions; minimizer; concentration; Reverse Hardy-Littlewood-Sobolev inequalities; interpolation; non-linear diffusion