Variational solutions to the total variation flow on metric measure spaces

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-07
Major/Subject
Mcode
Degree programme
Language
en
Pages
31
1-31
Series
Nonlinear Analysis, Theory, Methods and Applications, Volume 220
Abstract
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.
Description
Publisher Copyright: © 2022 The Author(s)
Keywords
Metric measure spaces, Parabolic Sobolev spaces, Parabolic variational problems, Sobolev spaces, Time mollifications
Other note
Citation
Buffa , V , Kinnunen , J & Pacchiano Camacho , C 2022 , ' Variational solutions to the total variation flow on metric measure spaces ' , Nonlinear Analysis, Theory, Methods and Applications , vol. 220 , 112859 , pp. 1-31 . https://doi.org/10.1016/j.na.2022.112859