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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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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Additional Information
  • Antonin Chambolle
  • Affiliation: CMAP, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
  • MR Author ID: 320037
  • ORCID: 0000-0002-9465-4659
  • Email:
  • Tim Laux
  • Affiliation: University of Bonn, Hausdorff Center for Mathematics, Villa Maria, Endenicher Allee 62, D-53115 Bonn, Germany
  • MR Author ID: 1181628
  • ORCID: 0000-0002-8084-4718
  • Email:
  • Received by editor(s): October 6, 2019
  • Received by editor(s) in revised form: September 30, 2020, and November 3, 2020
  • Published electronically: April 29, 2021
  • Additional Notes: This project was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC-2047/1 - 390685813
  • Communicated by: Ryan Hynd
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2943-2956
  • MSC (2020): Primary 35A15, 35R37; Secondary 49Q20, 76D27, 90B06, 35R35
  • DOI:
  • MathSciNet review: 4257806