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Existence of Ground States of Nonlocal-Interaction Energies

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journal contribution
posted on 01.05.2014, 00:00 by Robert Simione, Dejan SlepcevDejan Slepcev, Ihsan Topaloglu

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.


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