Global minimisers for anisotropic attractive-repulsive interactions

Kaib, Gunnar; Kang, Kyungkeun; Stevens, Angela

Abstract

We prove the existence of global minimisers for a class of attractive–repulsive interaction potentials that are in general not radially symmetric. The global minimisers 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 minimisers may neither be radial symmetric nor unique.