## Mullins-Sekerka as the Wasserstein flow of the perimeter

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- by Antonin Chambolle and Tim Laux PDF
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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), 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.## References

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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: antonin.chambolle@cmap.polytechnique.fr
**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: tim.laux@hcm.uni-bonn.de
- 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: https://doi.org/10.1090/proc/15401
- MathSciNet review: 4257806