%0 Journal Article
%T Periodic total variation flow of non-divergence type in Rn
%A Mi-Ho Giga
%A Yoshikazu Giga
%A Norbert Pozar
%J Mathematics
%D 2013
%I arXiv
%X We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a crystalline mean curvature. We establish a comparison principle, the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data.
%U http://arxiv.org/abs/1302.0618v1