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In their simplest form, the Caffarelli-Kohn-Nirenberg inequalities are a twoparameter family of inequalities. It has been known that there is a region inparameter space where the optimizers for the inequalities have broken symmetry.It has been shown recently that in the complement of this region the optimizersare radially symmetric. The ideas for the proof will be given.

Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities