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arXiv · 1910.02508

Mullins-Sekerka as the Wasserstein flow of the perimeter

Antonin Chambolle·Tim Laux
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Abstract

We prove the convergence of an implicit time discretization for the one-phase Mullins-Sekerka equation, possibly with additional non-local repulsion, 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 arguments from optimal transport, gradient flows & minimizing movements, and basic geometric measure theory.

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Antonin Chambolle, Tim Laux. 2019-10-06. Mullins-Sekerka as the Wasserstein flow of the perimeter. https://arxiv.org/abs/1910.02508

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