Under an energy convergence hypothesis, solutions of a heterogeneous Allen-Cahn equation with space-dependent wells converge to a BV solution of weighted mean curvature flow, and a weak-strong uniqueness principle holds.
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Convergence of a heterogeneous Allen-Cahn equation to weighted mean curvature flow
Under an energy convergence hypothesis, solutions of a heterogeneous Allen-Cahn equation with space-dependent wells converge to a BV solution of weighted mean curvature flow, and a weak-strong uniqueness principle holds.