On the definition of solution to the total variation flow
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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20
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Calculus of Variations and Partial Differential Equations, Volume 61, issue 1, pp. 1-20
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.Description
Funding Information: The first author would like to thank Heikki Hakkarainen, Panu Lahti and Olli Saari for several useful discussions on this topic over the years. Publisher Copyright: © 2021, The Author(s).
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Kinnunen, J & Scheven, C 2022, 'On the definition of solution to the total variation flow', Calculus of Variations and Partial Differential Equations, vol. 61, no. 1, 40, pp. 1-20. https://doi.org/10.1007/s00526-021-02142-y