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

Abstract

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.

References in corpus (1)

• Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

Cited by in corpus (1)

• Existence of extremal functions for a family of Caffarelli-Kohn-Nirenberg inequalities