Minimizers for an aggregation model with attractive-repulsive interaction
Analysis of PDEs
2023-11-27 v3 Mathematical Physics
Classical Analysis and ODEs
math.MP
Optimization and Control
Abstract
We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.
Cite
@article{arxiv.2307.13769,
title = {Minimizers for an aggregation model with attractive-repulsive interaction},
author = {Rupert L. Frank and Ryan W. Matzke},
journal= {arXiv preprint arXiv:2307.13769},
year = {2023}
}
Comments
16 pages; significant strengthening of the main result compared to the previous version