Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains

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Abstract

We study a singular limit problem of the Allen–Cahn equation with a homogeneous Neumann boundary condition on non-convex domains with smooth boundaries under suitable assumptions for initial data. The main result is the convergence of the time parametrized family of the diffused surface energy to Brakke’s mean curvature flow with a generalized right angle condition on the boundary of the domain.

Original languageEnglish
Pages (from-to)1485-1528
Number of pages44
JournalMathematische Annalen
Volume373
Issue number3-4
DOIs
Publication statusPublished - Apr 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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