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Local minimisers of a three-phase partition problem with triple junctions

Published online by Cambridge University Press:  14 November 2011

Peter Sternberg  and
William P. Zeimer
Peter Sternberg
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
William P. Zeimer
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
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Abstract

We establish the existence of isolated local minimisers to the problem of partitioning certain two-dimensional domains into three subdomains having least interfacial area. The solution we exhibit has the special property that the three boundaries of the minimising partition meet at a common point or “triple junction”. The configuration represents a likely candidate for a stable equilibrium in the dynamical problem of two-dimensional motion by curvature and also leads to the existence of local minimisers possessing triple junction structure to the energy associated with the vector Ginzburg–Landau and Cahn–Hilliard evolutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1059 - 1073
Copyright
Copyright © Royal Society of Edinburgh 1994

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