Variational solutions to the total variation flow on metric measure spaces. (July 2022) - Buffa, Vito; Kinnunen, Juha; Camacho, Cintia Pacchiano
Abstract: We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincaré inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and functions of bounded variation to prove a necessary and sufficient condition for a variational solution to be continuous at a given point.