On the symmetry of extremals for the Caffarelli-Kohn-Nirenberg inequalities

Jean Dolbeault (1) , Maria J. Esteban (1) , Michael Loss (2) , Gabriella Tarantello (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Mathematics - Georgia Institute of Technology
3 DIPMAT - Dipartimento di Matematica [Roma II]

In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal than two.

Mots clés: Hardy-Sobolev inequality; Caffarelli-Kohn-Nirenberg inequality; extremal functions; Kelvin transformation; Emden-Fowler transformation; radial symmetry; symmetry breaking

Domaines: Equations aux dérivées partielles [math.AP]

Jean Dolbeault, Maria J. Esteban, Michael Loss, Gabriella Tarantello. On the symmetry of extremals for the Caffarelli-Kohn-Nirenberg inequalities. Advanced Nonlinear Studies, 2009, 9, pp.713-727. ⟨hal-00402961v2⟩