Existence of Minimizers of Nonlocal Interaction Energies
Robert Simione, Dejan Slepčev, Ihsan Topaloğlu · arXiv (Cornell University) · 2014
Abstract. We investigate nonlocal-interaction energies on the space of probability measures. We establish sharp conditions for the existence of minimizers for a broad class of nonlocal-interaction energies. The condition is closely related to the notion of H-stability of pairwise interaction potentials in statistical mechanics. Our approach uses the direct method of calculus of variations. 1.