Variational solutions to the total variation flow on metric measure spaces

Vito Buffa, Juha Kinnunen*, Cintia Pacchiano Camacho

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 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.

Original languageEnglish
Article number112859
Pages (from-to)1-31
Number of pages31
JournalNonlinear Analysis, Theory, Methods and Applications
Volume220
DOIs
Publication statusPublished - Jul 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • Metric measure spaces
  • Parabolic Sobolev spaces
  • Parabolic variational problems
  • Sobolev spaces
  • Time mollifications

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