turkmath.org

In this talk I will present some recent results about the qualitative properties of extremal functions for functional inequalities. I will show that linear and nonlinear flows are a very good tool to do this in an optimal way. The main subject of my talk will be the symmetry of extremals for Caffarelli-Kohn-Nirenberg inequalities on the Euclidian space. But I will also explain how this method can be used to derive similar inequalities and results on Riemannian manifolds.