Symmetry of extremals of functional inequalities via spectral estimates   for linear operators
  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. 
Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE), Michael Loss
math.AP