Minimizers of Interaction Energies

Jose A. Carrillo De La Plata

(Imperial College)

Event: ERC Workshop on Optimal Transportation and Applications

Date: Oct 30, 2014, time: 11:15

Abstract. I will start by reviewing some recent results on qualitative properties of local
minimizers of the interaction energie to motivate the main topic of my talk: to discuss
global minimizers. We will show the existence of compactly supported global miminizers
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. An approach from
discrete to continuum is also quite nice under convexity assumptions on the potential.
This is based on three preprints/works in preparation one together with F. Patacchini,
J.A. Caizo, another one with M. Delgadino and A. Mellet, and finally with M. Chipot
and Y. Huang.