Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities
  In their simplest form, the Caffarelli-Kohn-Nirenberg inequalities are a two parameter family of inequalities. It has been known that there is a region in parameter space where the optimizers for the inequalities have broken symmetry. It has been shown recently that in the complement of this region the optimizers are radially symmetric. The ideas for the proof will be given. 
Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE), Michael Loss
math.AP