Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality

par María del Mar González Nogueras (Universidad Autónoma de Madrid)

mardi 15 déc. 2020, 14:00 → 15:00 Europe/Paris

Salle Fokko du Cloux (ICJ)

We will consider a fractional version of the classical Caffarelli-Kohn-Nirenberg inequality. We first study the existence and nonexistence of extremal solutions. Our next goal is to show some results for the symmetry and symmetry breaking region for the minimizers. In order to get these  we reformulate the inequality in cylindrical variables and so that we can use the non-local ODE theory previously developed by the authors for radial solutions. We also get non-degeneracy of critical points and uniqueness of minimizers in the radial symmetry class.