On a Quaternary Non-Local Isoperimetric Problem
Abstract
We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited spreading. Here we consider a limit in which three species are vanishingly small, but interactions are correspondingly large to maintain a nontrivial limit. In this limit two energy levels are distinguished: the highest order limit encodes information on the geometry of local structures as a three-component isoperimetric problem, while the second level describes the spatial distribution of components in global minimizers. Geometrical descriptions of limit configurations are derived.
Cite
@article{arxiv.2307.12504,
title = {On a Quaternary Non-Local Isoperimetric Problem},
author = {Stanley Alama and Lia Bronsard and Xinyang Lu and Chong Wang},
journal= {arXiv preprint arXiv:2307.12504},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1912.08971