Mullins-Sekerka as the Wasserstein flow of the perimeter

Antonin Chambolle; Tim Laux

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Mullins-Sekerka as the Wasserstein flow of the perimeter

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arxiv 1910.02508 v2 pith:ENON4TSB submitted 2019-10-06 math.AP math.OC

Antonin Chambolle , Tim Laux This is my paper · ORCID

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keywords equationmullins-sekerkaoptimaladditionalanalarchargumentarguments

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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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