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Jounal of mathematical physics 53(P) (2012) 095204
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Symmetry of extremals of functional inequalities via spectral estimates for linear operators
Jean Dolbeault1, Maria J. Esteban1, Michael Loss2

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.
1 :  CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 :  School of Mathematics - Georgia Institute of Technology
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