Variational solutions to the total variation flow on metric measure spaces Article Swipe

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Vito Buffa , Juha Kinnunen , Cintia Pacchiano Camacho ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2109.11908 · OA: W4286962316

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.