Singular perturbation of a class of non-convex functionals

Models involving singular perturbation to a non-convex potential energy play a very important role in describing phase transitions, e.g. the celebrated Cahn-Hillard model where a two-well potential energy functional (i.e., the potential has two zeros) is perturbed by the L-2-norm of the gradient. Many variants of this model have been studied. In this paper, we perturb a general multi-well energy functional by the L-2-norm of a higher gradient Hessian of arbitrary order and study its Gamma(L-1)-limit. As expected, the limit functional assigns different surface energy densities to interfaces between different phases and computes the total energy. (C) 2002 Elsevier Science Ltd. All rights reserved.