Symmetry of extremals of functional inequalities via spectral estimates for linear operators
Résumé
We prove new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities in any dimension larger or equal than 2, in a range of parameters for which no explicit results of symmetry were previously known.
Mots clés
Hardy-Sobolev inequality
Caffarelli-Kohn-Nirenberg inequality
extremal functions
Kelvin transformation
Emden-Fowler transformation
radial symmetry
symmetry breaking
rigidity
Lieb-Thirring inequalities
generalized Poincaré inequalities
estimates of the best constants
cylinder
Riemannian manifold
Ricci curvature
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