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Kinnunen, Juha; Scheven, Christoph

On the definition of solution to the total variation flow

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  • Media type: E-Article
  • Title: On the definition of solution to the total variation flow
  • Contributor: Kinnunen, Juha; Scheven, Christoph
  • Published: Springer Science and Business Media LLC, 2022
  • Published in: Calculus of Variations and Partial Differential Equations, 61 (2022) 1
  • Language: English
  • DOI: 10.1007/s00526-021-02142-y
  • ISSN: 0944-2669; 1432-0835
  • Keywords: Applied Mathematics ; Analysis
  • Origination:
  • Footnote:
  • Description: 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.