{H}ardy-{S}obolev inequalities with singularities on non smooth boundary. {P}art 2: {I}nfluence of the global geometry in small dimensions - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

{H}ardy-{S}obolev inequalities with singularities on non smooth boundary. {P}art 2: {I}nfluence of the global geometry in small dimensions

Résumé

We consider Hardy-Sobolev nonlinear equations on domains with singularities. We introduced this problem in Cheikh-Ali [4]. Under a local geometric hypothesis, namely that the generalized mean curvature is negative (see (6) below), we proved the existence of extremals for the relevant Hardy-Sobolev inequality for large dimensions. In the present paper, we tackle the question of small dimensions that was left open. We introduce a "mass", that is a global quantity, the positivity of which ensures the existence of extremals in small dimensions. As a byproduct, we prove the existence of solutions to a perturbation of the initial equation via the Mountain Pass Lemma.
Fichier principal
Vignette du fichier
Cheikh-Ali_Mass_HardySobolev.pdf (455.02 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02048901 , version 1 (25-02-2019)
hal-02048901 , version 2 (05-10-2020)

Identifiants

  • HAL Id : hal-02048901 , version 1

Citer

Hussein Cheikh Ali. {H}ardy-{S}obolev inequalities with singularities on non smooth boundary. {P}art 2: {I}nfluence of the global geometry in small dimensions. 2019. ⟨hal-02048901v1⟩
114 Consultations
112 Téléchargements

Partager

Gmail Facebook X LinkedIn More