Anisotropic total variation flow of non-divergence type on a higher dimensional torus

Abstract

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.

27 pages

References in corpus (2)

• Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature
• Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature