On a quaternary nonlocal isoperimetric problem

Alama, Stanley; Bronsard, Lia; Lu, Xinyang; Wang, Chong

doi:10.1090/qam/1675

Authors: Stanley Alama, Lia Bronsard, Xinyang Lu and Chong Wang
Journal: Quart. Appl. Math. 82 (2024), 97-113
MSC (2020): Primary 49J45, 49J10, 49Q05
DOI: https://doi.org/10.1090/qam/1675
Published electronically: July 3, 2023
MathSciNet review: 4695277
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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.

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