MULLINS-SEKERKA AS THE WASSERSTEIN FLOW OF THE PERIMETER

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02306665
Contributor : Antonin Chambolle <>
Submitted on : Sunday, October 6, 2019 - 8:50:02 PM
Last modification on : Thursday, October 10, 2019 - 1:17:31 AM

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  • HAL Id : hal-02306665, version 1

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Antonin Chambolle, Tim Laux. MULLINS-SEKERKA AS THE WASSERSTEIN FLOW OF THE PERIMETER. 2019. ⟨hal-02306665⟩

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