Variational characterization of interior interfaces in phase transition models on convex plane domains
C. E. Garza-Hume, Pablo Padilla · DOAJ (DOAJ: Directory of Open Access Journals) · 2003
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.