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.
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© Cambridge University Press 2019.
All Science Journal Classification (ASJC) codes
- Applied Mathematics