Higher Multiplicity in the One-Dimensional Allen-Cahn Action Functional
Preprint Series # 821
Reznikoff, Maria G and Tonegawa, Yoshihiro Higher Multiplicity in the One-Dimensional Allen-Cahn Action Functional. (2006);
We prove the ¡-convergence of the Allen-Cahn action functional in
the sharp-interface limit. In previous work, good lower bounds were
developed under the assumption of single-multiplicity, but the bounds
deteriorated in the case of higher-multiplicity interfaces. We develop
improved bounds by working directly with the limiting energy measures.