IUMJ

Title: Higher multiplicity in the one-dimensional Allen-Cahn action functional

Authors: Maria G. Westdickenberg and Yoshihiro Tonegawa

Issue: Volume 56 (2007), Issue 6, 2935-2990

Abstract:

We prove the $\Gamma$-convergence of the one-dimensional Allen-Cahn action functional in the sharp-interface limit. In previous work, a good lower bound was developed under the assumption of single multiplicity, but the bound deteriorated in the case of higher multiplicity interfaces. We develop an improved bound by working directly with the limiting energy measures.