arXiv:2109.11908 Abstract | arXiv Analytics

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Variational solutions to the total variation flow on metric measure spaces

Vito Buffa, Juha Kinnunen, Cintia Pacchiano Camacho

Published 2021-09-24, updated 2022-02-12Version 2

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.

Categories: math.AP, math.FA, math.MG

Subjects: 49J27, 49J40, 49J45, 30L99, 35A15

Keywords: total variation flow, metric measure spaces, variational solution, poincare inequality, purely variational approach

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