Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants

Details Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants

2010-09-28

arxiv.org/abs/1009.5619v1

Mathematics

Analysis of PDEs

Scientific paper

This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These results have been obtained in a series of papers in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented from a new viewpoint.

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