Preprint 32/2019

Global Minimizers for Anisotropic Attractive-Repulsive Interactions

Gunnar Kaib, Kyungkeun Kang, and Angela Stevens

Contact the author: Please use for correspondence this email.
Submission date: 21. Mar. 2019 (revised version: August 2019)
Pages: 18
MSC-Numbers: 35A15, 35K65
Keywords and phrases: anisotropic attractive-repulsive interaction, global minimizers
Download full preprint: PDF (391 kB)

We prove existence of global minimizers for a class of attractive-repulsive interaction potentials that are in general not radially symmetric. The global minimizers have compact support. For potentials including degenerate power-law diffusion the interaction potential can be unbounded from below. Further, a formal calculation indicates that for non-symmetric potentials global minimizers may neither be radial symmetric nor unique.

04.09.2019, 14:40