Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities

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Date
2016
Titre de la collection
Cahier de recherche CEREMADE, Université Paris-Dauphine
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https://hal.archives-ouvertes.fr/hal-01286546
Indexation documentaire
Analyse
Subject
rigidity results; symmetry breaking; optimal constants; Caffarelli-Kohn-Nirenberg inequalities; symmetry; fast diffusion equation
URI
https://basepub.dauphine.fr/handle/123456789/17052
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Auteur
Dolbeault, Jean
Esteban, Maria J.
Loss, Michael
Type
Document de travail / Working paper
Nombre de pages du document
9
Résumé en anglais
In their simplest form, the Caffarelli-Kohn-Nirenberg inequalities are a two parameter family of inequalities. It has been known that there is a region in parameter space where the optimizers for the inequalities have broken symmetry. It has been shown recently that in the complement of this region the optimizers are radially symmetric. The ideas for the proof will be given.