论文标题
最大程度地减少强迫各向异性平均曲率流动流动的运动
Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities
论文作者
论文摘要
在对各向异性家族的适当假设下，我们证明存在薄弱的全局$ \ frac {1} {n+1} $-Hölder在时间平均曲率流中连续均匀曲率流，并使用最小化运动的方法在任何维度中的各向异性分区的动机。当存在合适的驱动力时，将结果扩展到案例。在具有相同各向异性和相同移动性的分区的情况下，我们将Hölder指数提高到$ \ frac12 $，并在此设置中提供了较弱的比较结果，用于较弱的各向异性平均曲率流动和各向异性平均值曲率曲率曲率两相流动。
Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global $\frac{1}{n+1}$-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 $\frac12$ in the case of partitions with the same anisotropy and the same mobility and provide a weak comparision result in this setting for a weak anisotropic mean curvature flow of a partition and an anisotropic mean curvature two-phase flow.
