论文标题
平面溶液与保持平均曲率流量的一致性
Consistency of the flat flow solution to the volume preserving mean curvature flow
论文作者
论文摘要
我们考虑通过离散最小化移动方案获得的平坦流解决方案，从c^{1,1} -Remular集合开始的体积保留平均曲率流量。我们证明了一致性原则，该原则指出（任何）这种平坦的流量只要后者存在，就与经典解决方案一致。特别是，扁平流是独一无二的，直到第一个单一的时间。我们通过证明扁平流的离散时间近似的全部规律性来获得结果，从而相对于时间离散化的规律性估计值稳定。在平均曲率流的情况下，我们的方法也可以应用，因此它提供了一个替代证明，而不是依赖比较原理，因为平面流解决方案与C^{1,1}的经典解决方案之间的一致性。
We consider the flat flow solution, obtained via discrete minimizing movement scheme, to the volume preserving mean curvature flow starting from C^{1,1}-regular set. We prove the consistency principle which states that (any) such flat flow agrees with the classical solution as long as the latter exists. In particular, the flat flow is unique and smooth up to the first singular time. We obtain the result by proving the full regularity for the discrete time approximation of the flat flow such that the regularity estimates are stable with respect to the time discretization. Our method can also be applied in the case of the mean curvature flow and thus it provides an alternative proof, not relying on comparison principle, for the consistency between the flat flow solution and the classical solution for C^{1,1}-regular initial sets.
