On the definition of solution to the total variation flow

Juha Kinnunen; Christoph Scheven

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arXiv · 2106.05711

On the definition of solution to the total variation flow

Juha Kinnunen·Christoph Scheven

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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.

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Juha Kinnunen, Christoph Scheven. 2021-06-10. On the definition of solution to the total variation flow. https://arxiv.org/abs/2106.05711

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