Existence of Ground States of Nonlocal-Interaction Energies

Abstract

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.

This version is to appear in the J Stat Phys

References in corpus (2)

• On global minimizers of repulsive-attractive power-law interaction energies
• Regularity of local minimizers of the interaction energy via obstacle problems

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• Equilibria for an aggregation model with two species
• Minimizers of nonlocal interaction functional with exogenous potential
• Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
• Continuity of critical points for 1-dimensional non-local energies
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