论文标题
晶体平均曲率流动的粘度溶液，具有不均匀的驱动力项
Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term
论文作者
论文摘要
考虑到具有不均匀驱动力项的一般纯晶体平均曲率流动方程。当驱动力项在及时均匀地统一时，驱动力项是连续和空间上的，建立了水平集的独特存在。通过引入适当的解决方案概念，可以为包括级别设置方程在内的方程式建立连续解决方案的比较原理。解决方案的存在是通过稳定性和近似问题获得的。建立了近似解决方案的必要等级。应当指出的是，晶体曲率的值不仅可以取决于不断发展的表面的几何形状，而且还取决于驱动力，如果它在空间上不均匀。
A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz uniformly in time. By introducing a suitable notion of a solution a comparison principle of continuous solutions is established for equations including the level set equations. An existence of a solution is obtained by stability and approximation by smoother problems. A necessary equi-continuity of approximate solutions is established. It should be noted that the value of crystalline curvature may depend not only on the geometry of evolving surfaces but also on the driving force if it is spatially inhomogeneous.
