Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 101, pp. 1-6.

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

Authors: Clara E. Garza-Hume (UNAM, Mexico City, Mexico)
  Pablo Padilla (UNAM, Mexico City, Mexico)

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.