Special Session 10: 

Minimisers and Critical Points of Aggregation Diffusion Equations

Matias g Delgadino
Imperial College
Argentina
Co-Author(s):    Carrillo, Patacchini
Abstract:
We analyse free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. We derive conditions for the energy to allow for critical points or global minimisers. In the fast diffusion regime, we prove the reversed Hardy-Littlewood-Sobolev inequality and we discuss the condensation phenomena for minimisers.