Variational characterization of interior interfaces in phase transition models on convex plane domains
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We consider the singularly perturbed Allen-Cahn equation on a strictly convex plane domain. We show that when the perturbation parameter tends to zero there are solutions having a transition layer that tends to a straight line segment. This segment can be characterized as the shortest path intersecting the boundary orthogonally at two points.
CitationGarza-Hume, C. E., & Padilla, P. (2003). Variational characterization of interior interfaces in phase transition models on convex plane domains. Electronic Journal of Differential Equations, 2003(101), pp. 1-6.
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