  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.
