Geometry of minimizers for the interaction energy with mildly repulsive potentials

Abstract

We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ and mildly repulsive at the origin; moreover, if the minimizer is global, then its support is finite. In addition, for some class of potentials we prove the validity of a uniform upper bound on the cardinal of the support of a global minimizer. Finally, in the one-dimensional case, we give quantitative bounds.

In this updated version we corrected a couple of misprints and added details to the proof of Lemma 2.4. 10 pages, 1 figure

References in corpus (1)

• Existence of Ground States of Nonlocal-Interaction Energies

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