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arXiv · 2109.11908

Variational solutions to the total variation flow on metric measure spaces

Vito Buffa·Juha Kinnunen·Cintia Pacchiano Camacho
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Abstract

We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincar\'e 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.

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Vito Buffa, Juha Kinnunen, Cintia Pacchiano Camacho. 2021-09-24. Variational solutions to the total variation flow on metric measure spaces. https://doi.org/10.1016/j.na.2022.112859

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