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.

中文翻译：

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最小化具有流动性的分区的强制各向异性平均曲率流的运动

在对各向异性族的适当假设下，我们证明了弱全局 1/(n+1)-Hölder 使用最小化运动的方法在时间上连续平均曲率流，在任何维度上具有有界各向异性分区的迁移率。结果扩展到存在适当驱动力的情况。在具有相同各向异性和相同流动性的分区的情况下，我们将 Hölder 指数提高到 1/2，并在此设置中为分区的弱各向异性平均曲率流和各向异性平均曲率两相流提供了较弱的比较结果.