Date
2012
Lien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00496936/fr/
Indexation documentaire
Probabilités et mathématiques appliquées
Subject
Caffarelli-Kohn-Nirenberg inequality; Hardy-Sobolev inequality; Sobolev spaces; existence; symmetry breaking; compactness; radial symmetry; Emden-Fowler transformation; Kelvin transformation; extremal functions; logarithmic Hardy inequality
Nom de la revue
Proceedings of the Royal Society of Edinburgh. Section A, Mathematical and Physical Sciences
Volume
142
Numéro
4
Date de publication
2012
Pages article
745-767
Nom de l'éditeur
Cambridge University Press
Auteur
Dolbeault, Jean
Esteban, Maria J.
Type
Article accepté pour publication ou publié
Résumé en anglais
We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which the optimal constants are achieved by extremal functions. The comparison of these optimal constants with the optimal constants of Gagliardo-Nirenberg interpolation inequalities and Gross' logarithmic Sobolev inequality, both without weights, gives a general criterion for such an existence result in some particular cases.
