  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.
