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Anisotropic and crystalline mean curvature flow of mean-convex sets

By Antonin Chambolle and Matteo Novaga

Abstract

We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive anisotropic mean curvature. We show that such condition is preserved by the scheme, and we prove the strict convergence in BV of the time-integrated perimeters of the approximating evolutions, extending a recent result of De Philippis and Laux to the anisotropic setting. We also prove uniqueness of the flat flow obtained in the limit

Topics: Mathematics - Analysis of PDEs, Mathematics - Optimization and Control
Year: 2020
OAI identifier: oai:arXiv.org:2004.00270

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