Mullins-Sekerka as the Wasserstein flow of the perimeter

Chambolle, Antonin; Laux, Tim

doi:10.1090/proc/15401

Mullins-Sekerka as the Wasserstein flow of the perimeter
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by Antonin Chambolle and Tim Laux PDF

Proc. Amer. Math. Soc. 149 (2021), 2943-2956 Request permission

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), pp. 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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