Existence of Ground States of Nonlocal-Interaction Energies
  We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that this condition is closely related to the notion of stability (i.e. $H$-stability) of pairwise interaction potentials. Our approach uses the direct method of the calculus of variations. 
Robert Simione, Dejan Slep\v{c}ev and Ihsan Topaloglu
math.AP