具有非均匀驱动力项的晶体中曲率流的黏性解
Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term
摘要：
考虑了一个一般的带非均匀驱动力项的纯晶体中曲率流动方程。当驱动力项在空间上连续且在时间上一致Lipschitz时，证明了水平集流的唯一存在性。通过引入适当的解的概念，建立了包括水平集方程在内的方程的连续解的比较原理。通过稳定性和光滑问题的逼近得到解的存在性。建立了近似解的必要等连续性。应该注意的是，晶体曲率的值可能不仅取决于演化表面的几何形状，而且取决于驱动力，如果它是空间不均匀的。
英文摘要：
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.
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