UBC Math. Phys. Seminar: Norbert Pozar (Cancelled)

In this talk I will give an overview of the notion of viscosity solutions for the crystalline mean curvature flow in an arbitrary dimension, introduced recently in joint work with Yoshikazu Giga from the University of Tokyo. This problem serves as a model of crystal growth but it also has applications in image processing and related fields. Its level set formulation leads to a nonlocal, very singular parabolic equation with non-smooth, faceted solutions to which the standard viscosity theory does not apply. We introduce a reduced class of faceted test functions and show that they are sufficient to establish the comparison principle as well as an existence result for a rather general class of problems with the crystalline mean curvature.