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Journal Articles Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Year : 2020

Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities

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Abstract

Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global 1/(n+1)-Hölder continuous in time mean curvature flow with mobilities of a bounded anisotropic partition in any dimension using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We improve the Hölder exponent to 1/2 in the case of partitions with the same anisotropy and the same mobility and provide a weak comparison result in this setting for a weak anisotropic mean curvature flow of a partition and an anisotropic mean curvature two-phase flow.

Dates and versions

hal-02959423 , version 1 (06-10-2020)

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Giovanni Bellettini, Antonin Chambolle, Shokhrukh Kholmatov. Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2020, 151 (4), pp.1135--1170. ⟨10.1017/prm.2020.53⟩. ⟨hal-02959423⟩
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