CRYSTALLINE SURFACE DIFFUSION FLOW FOR GRAPH-LIKE CURVES

This paper studies a fourth-order crystalline curvature ow for a curve represented by the graph of a spatially periodic function. This is a spe- cial example of general crystalline surface diffusion flow. We consider a special class of piecewise linear functions and calculate its speed. We introduce notion of firmness and prove that the solution stays firm if initially it is firm at least for a short time. We also give an example that a facet (flat part) may split if the initial profile is not firm. Moreover, an example of facet-merging is given as well as several estimates for the speed of each facet