%0 Journal Article
%T Anisotropic total variation flow of non-divergence type on a higher dimensional torus
%A Mi-Ho Giga
%A Yoshikazu Giga
%A Norbert Pozar
%J Mathematics
%D 2013
%I arXiv
%X We extend the theory of viscosity solutions to a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of an arbitrary dimension with diffusion given by an anisotropic total variation energy. We give a proof of a comparison principle, an outline of a proof of the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data, which extend the results recently obtained by the authors.
%U http://arxiv.org/abs/1305.5904v1