Global Minimizers for Anisotropic Attractive-Repulsive Interactions
Gunnar Kaib, Kyungkeun Kang, and Angela Stevens
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Submission date: 21. Mar. 2019 (revised version: August 2019)
MSC-Numbers: 35A15, 35K65
Keywords and phrases: anisotropic attractive-repulsive interaction, global minimizers
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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.