Preprint 32/2019

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)
Pages: 18
Bibtex
MSC-Numbers: 35A15, 35K65
Keywords and phrases: anisotropic attractive-repulsive interaction, global minimizers
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Abstract:
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