论文标题
平均凸集的平均曲率流的阈值方案的强收敛
Strong convergence of the thresholding scheme for the mean curvature flow of mean convex sets
论文作者
论文摘要
在这项工作中，我们分析了Merriman，Bence和Osher的阈值方案，这是平均曲率流的时间离散化。我们局限于两相设置和平均凸初始条件。从最小化的运动解释和Otto的最小化运动解释的意义上，我们显示了近似的时间集成能，以收敛到极限的时间集成能。作为推论，OTTO的条件收敛结果和其中一位作者在两相平均凸情况下变得无条件。我们的结果足以处理该方案向各向异性流的扩展，可以为其选择非负核。
In this work, we analyze Merriman, Bence and Osher's thresholding scheme, a time discretization for mean curvature flow. We restrict to the two-phase setting and mean convex initial conditions. In the sense of the minimizing movements interpretation of Esedoglu and Otto we show the time-integrated energy of the approximation to converge to the time-integrated energy of the limit. As a corollary, the conditional convergence results of Otto and one of the authors become unconditional in the two-phase mean convex case. Our results are general enough to handle the extension of the scheme to anisotropic flows for which a non-negative kernel can be chosen.
