Dept. Math, Hokkaido Univ. EPrints Server

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);

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Abstract

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.

Item Type:Preprint
Subjects:49-xx CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
ID Code:1660