Electron. J. Diff. Eqns., Vol. 2003(2003), No. 101, pp. 1-6.

Variational characterization of interior interfaces in phase transition models on convex plane domains

Clara E. Garza-Hume & Pablo Padilla

Abstract:
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.

Submitted July 15, 2003. Published October 2, 2003.
Math Subject Classifications: 49Q20, 35J60, 82B26.
Key Words: Phase transition, singularly perturbed Allen-Cahn equation, convex plane domain, variational methods, transition layer, Gauss map, geodesic, varifold.

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Clara E. Garza-Hume
Department of Applied Mathematics
UNAM, Mexico City, Mexico
email: clara@mym.iimas.unam.mx
Pablo Padilla
Department of Applied Mathematics
UNAM, Mexico City, Mexico
email: pablo@mym.iimas.unam.mx

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