2024-03-28T22:41:28Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696292022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Higher Multiplicity in the One-Dimensional Allen-Cahn Action FunctionalReznikoff, Maria GTonegawa, YoshihiroAllen-Cahn equationstochastic partial di®erential equationslarge deviation theoryaction minimizationsharp-interface limits¡-convergence410We 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69629info:doi/10.14943/83971https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69629/1/pre821.pdfHokkaido University Preprint Series in Mathematics8211552006-12-15engpublisher