Convergence of the Allen-Cahn equation with Neumann boundary conditions
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🧮 math.AP
math.DG
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boundaryallen-cahnconditionsenergyequationlimitneumannangle
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We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.
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