On the definition of solution to the total variation flow

Juha Kinnunen, Christoph Scheven*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
43 Downloads (Pure)

Abstract

We show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under some restrictions on the boundary data. The key ingredient in the argument is a duality result for the total variation functional, which is based on an approximation of the total variation by area-type functionals.

Original languageEnglish
Article number40
Pages (from-to)1-20
Number of pages20
JournalCalculus of Variations and Partial Differential Equations
Volume61
Issue number1
DOIs
Publication statusPublished - Feb 2022
MoE publication typeA1 Journal article-refereed

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