On the motion by singular interfacial energy
On the motion by singular interfacial energy
复制标题
奇异界面能运动
DOI：
10.1007/bf03168572
复制
发表时间：
2000
影响因子：
0.9
通讯作者：
P. Rybka
中科院分区：
文献类型：
--
作者：
Y. Giga;M. Paolini;P. Rybka
具有奇异界面能的各向异性曲率流方程对于很好地理解相边界的运动非常重要。如果能量和界面表面光滑，则界面速度将等于能量梯度。然而，在非光滑晶体能量的情况下，事情就没那么简单了。但众所周知，如果界面是二维空间中的曲线，则速度的唯一梯度表征是可能的。在本文中，我们通过引入几何次微分并表征速度，提出了三维空间中的解的概念。我们还给出了有关小平面（界面的平坦部分）上的 Cahn-Hoffman 矢量场问题的反例。
Anisotropic curvature flow equations with singular interfacial energy are important for good understanding of motion of phase-boundaries. If the energy and the interfacial surface were smooth, then the speed of the interface would be equal to the gradient of the energy. However, this is not so simple in the case of non-smooth crystalline energy. But it’s well-known that a unique gradient characterization of the velocity is possible if the interface is a curve in the two-dimensional space.In this paper we propose a notion of solution in the three-dimensional space by introducing geometric subdifferentials and characterizing the speed. We also give a counterexample to a problem concerning the Cahn-Hoffman vector field on a facet, a flat portion of the interface.