Generalized logarithmic Hardy-Littlewood-Sobolev inequality - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Generalized logarithmic Hardy-Littlewood-Sobolev inequality

Résumé

This paper is devoted to logarithmic Hardy-Littlewood-Sobolev inequalities in the two-dimensional Euclidean space, in presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter, with two regimes. The attractive regime reflects the standard logarithmic Hardy-Littlewood-Sobolev inequality. The second regime corresponds to a reverse inequality, with the opposite sign in the convolution term, that allows us to bound the free energy of a drift-diffusion-Poisson system from below. Our method is based on an extension of an entropy method proposed by E. Carlen, J. Carrillo and M. Loss, and on a nonlinear diffusion equation.
Fichier principal
Vignette du fichier
LogHLS.pdf (132.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02281279 , version 1 (09-09-2019)
hal-02281279 , version 2 (21-11-2019)
hal-02281279 , version 3 (24-12-2019)

Identifiants

Citer

Jean Dolbeault, Xingyu Li. Generalized logarithmic Hardy-Littlewood-Sobolev inequality. 2019. ⟨hal-02281279v1⟩
240 Consultations
198 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More