On the definition of solution to the total variation flow-Reference-Cited by-同舟云学术

On the definition of solution to the total variation flow

Published:2022-01-16 Issue:1 Volume:61 Page:
ISSN:0944-2669
Container-title:Calculus of Variations and Partial Differential Equations
language:en
Short-container-title:Calc. Var.

Author:

Kinnunen Juha,Scheven Christoph^ORCID

Abstract

AbstractWe 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.

Funder

Universität Duisburg-Essen

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s00526-021-02142-y.pdf

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