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

摘要

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