MULLINS-SEKERKA AS THE WASSERSTEIN FLOW OF THE PERIMETER
Résumé
We prove the convergence of an implicit time discretization for the Mullins-Sekerka equation proposed in [F. Otto, Arch. Rational Mech. Anal. 141 (1998) 63-103]. Our simple argument shows that the limit satisfies the equation in a distributional sense as well as an optimal energy-dissipation relation. The proof combines simple arguments from optimal transport, gradient flows & minimizing movements, and basic geometric measure theory.
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