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Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities

Dolbeault, Jean; Esteban, Maria J.; Loss, Michael (2016), Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities. https://basepub.dauphine.fr/handle/123456789/17052

Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01286546
Date
2016
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
9
Metadata
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Author(s)
Dolbeault, Jean cc

Esteban, Maria J. cc

Loss, Michael
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.
Subjects / Keywords
rigidity results; symmetry breaking; optimal constants; Caffarelli-Kohn-Nirenberg inequalities; symmetry; fast diffusion equation