Garza-Hume, Clara E.Padilla, Pablo2021-01-272021-01-272003-10-02Garza-Hume, C. E., & Padilla, P. (2003). Variational characterization of interior interfaces in phase transition models on convex plane domains. <i>Electronic Journal of Differential Equations, 2003</i>(101), pp. 1-6.1072-6691https://hdl.handle.net/10877/13152We 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.Text6 pages1 file (.pdf)enAttribution 4.0 InternationalPhase transitionsSingularly perturbed Allen-Cahn equationConvex plane domainVariational methodsTransition layerGauss mapGeodesicVarifoldArticle