Calculus of Variations and Geometric Measure Theory
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V. Buffa - J. Kinnunen - C. Pacchiano Camacho

Variational solutions to the total variation flow on metric measure spaces

created by buffa on 29 Sep 2021

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Submitted Paper

Inserted: 29 sep 2021
Last Updated: 29 sep 2021

Year: 2021

ArXiv: 2109.11908 PDF

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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