论文标题
图形非本地平均曲率流的短时间存在和平滑度
Short time existence and smoothness of the nonlocal mean curvature flow of graphs
论文作者
论文摘要
我们考虑了整个图的几何进化问题，该图是通过分数平均曲率移动的。为此，我们研究了图函数家族满足的相关非局部准线性演化方程。我们使用分析性分析方法，短时间存在，独特性和最佳的Hölder规律性在非局部方程的经典解决方案的时间和空间上，具体取决于初始图的规律性。该方法还产生$ C^\ Infty- $平滑度的估计值，以实现积极时代的发展图。
We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. For this, we study the associated nonlocal quasilinear evolution equation satisfied by the family of graph functions. We establish, using an analytic semigroup approach, short time existence, uniqueness and optimal Hölder regularity in time and space of classical solutions of the nonlocal equation, depending on the regularity of the initial graph. The method also yields $C^\infty-$smoothness estimates of the evolving graphs for positive times.
