On the definition of solution to the total variation flow
Analysis of PDEs
2021-10-25 v3
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.
Keywords
Cite
@article{arxiv.2106.05711,
title = {On the definition of solution to the total variation flow},
author = {Juha Kinnunen and Christoph Scheven},
journal= {arXiv preprint arXiv:2106.05711},
year = {2021}
}