Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 14-CNA-013 Existence of Minimizers of Nonlocal Interaction Energies Robert SimioneDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PArsimione@andrew.cmu.edu Dejan SlepčevDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213slepcev@andrew.cmu.edu Ihsan TopalogluDepartment of Mathematics and Statistics McGill University Montreal, QC Canadaitopaloglu@math.mcgill.caAbstract: 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.Get the paper in its entirety as  14-CNA-013.pdf