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We study a singular limit problem of the Allen-Cahn equation with thehomogeneous Neumann boundary condition on non-convex domains with smoothboundaries under suitable assumptions for initial data. The main result is theconvergence of the time parametrized family of the diffused surface energy toBrakke's mean curvature flow with a generalized right angle condition on theboundary of the domain.

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