Mullins-Sekerka as the Wasserstein flow of the perimeter
Analysis of PDEs
2020-10-01 v2 Optimization and Control
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) 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.
Keywords
Cite
@article{arxiv.1910.02508,
title = {Mullins-Sekerka as the Wasserstein flow of the perimeter},
author = {Antonin Chambolle and Tim Laux},
journal= {arXiv preprint arXiv:1910.02508},
year = {2020}
}
Comments
13 pages, expanded some remarks