Minimizers for an aggregation model with attractive-repulsive interaction

Autor:	Frank, Rupert L., Matzke, Ryan W.
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages; significant strengthening of the main result compared to the previous version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.13769 Zobrazit plný text záznamu View this record from Arxiv