### arXiv:1911.02539 [math.AP]AbstractReferencesReviewsResources

#### On the Strong Attraction Limit for a Class of Nonlocal Interaction Energies

Almut Burchard, Rustum Choksi, Elias Hess-Childs

Published 2019-11-06Version 1

This note concerns the problem of minimizing a certain family of nonlocal energy functionals over measures on $\mathbb{R}^n$, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral over pair interactions of attractive-repulsive type. The interaction kernel is a sum of competing power law potentials with attractive powers $\alpha\in(0,\infty)$ and repulsive powers associated with Riesz potentials. The strong attraction limit $\alpha\rightarrow\infty$ is addressed via Gamma-convergence, and minimizers of the limit are characterized in terms of an isodiametric capacity problem.

**Comments:**12 pages, 7 figures

**Categories:**math.AP

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