Variational solutions to the total variation flow on metric measure spaces
Analysis of PDEs
2023-05-01 v2 Functional Analysis
Metric Geometry
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.
Keywords
Cite
@article{arxiv.2109.11908,
title = {Variational solutions to the total variation flow on metric measure spaces},
author = {Vito Buffa and Juha Kinnunen and Cintia Pacchiano Camacho},
journal= {arXiv preprint arXiv:2109.11908},
year = {2023}
}