University of Marseille
Title: Nonlocal phase transitions and minimal surfaces
In this talk, I will report on some recent works dealing with a fractional version of the Allen-Cahn equation. I will investigate the symmetry properties of the solutions, in connection with a conjecture by De Giorgi (in the local case). I will explicitely explain the connections with new non local minimal surfaces introduced by Caffarreli, Roquejoffre and Savin.