J. A. Carrillo: Minimizing Interaction Energies

Abstract: I will start by reviewing some recent results on qualitative properties of local minimizers of the interaction energies to motivate the main topic of my talk: to discuss global minimizers. We will show the existence of compactly supported global minimizes under quite mild assumptions on the potential in the complementary set of classical H-stability in statistical mechanics. A strong connection with the classical obstacle problem appears very useful when the singularity is strong enough at zero.