Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities

Thumbnail
Date
2016
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01286546
Dewey
Analyse
Sujet
rigidity results; symmetry breaking; optimal constants; Caffarelli-Kohn-Nirenberg inequalities; symmetry; fast diffusion equation
URI
https://basepub.dauphine.fr/handle/123456789/17052
Collections
Metadata
Show full item record
Author
Dolbeault, Jean
Esteban, Maria J.
Loss, Michael
Type
Document de travail / Working paper
Item number of pages
9
Abstract (EN)
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.