Higher Multiplicity in the One-Dimensional Allen-Cahn Action Functional
نویسندگان
چکیده
We prove the Γ-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.
منابع مشابه
The Allen-cahn Action Functional in Higher Dimensions
Abstract. The Allen–Cahn action functional is related to the probability of rare events in the stochastically perturbed Allen–Cahn equation. Formal calculations suggest a reduced action functional in the sharp interface limit. We prove in two and three space dimensions the corresponding lower bound. One difficulty is that diffuse interfaces may collapse in the limit. We therefore consider the l...
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