LOCAL MINIMIZERS OF A 3-PHASE PARTITION PROBLEM WITH TRIPLE JUNCTIONS

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.