26887 articles – 20547 references  [version française]
Detailed view Article in peer-reviewed journal
Jounal of mathematical physics 53(P) (2012) 095204
Available versions:
Attached file list to this document: 
DEL-26-09-2011-hal.pdf(256.5 KB)
DEL-26-09-2011-hal.ps(1.1 MB)
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