26 jun 2015 -- 15:15
Aula 2001, Dip. Matematica, Università degli Studi di Roma “Tor Vergata”, Roma
Abstract.
In this talk I will present recent results, obtained in collaboration with J. Dolbeault and M. Loss, proving the radial symmetry of the optimizers of Caffarelli-Kohn-Nirenberg inequalities whenever they are local minima in the full functional space. These results are optimal and close a series of works proving partial results. The method used to obtain this result, which actually proves the uniqueness of positive solutions for the corresponding Euler-Lagrange equations, is based on a nonlinear fast diffusion flow which is applied around any positive solution to explore the energy landscape around it.