TY - JOUR
T1 - On the definition of solution to the total variation flow
AU - Kinnunen, Juha
AU - Scheven, Christoph
N1 - 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).
PY - 2022/2
Y1 - 2022/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122938969&partnerID=8YFLogxK
U2 - 10.1007/s00526-021-02142-y
DO - 10.1007/s00526-021-02142-y
M3 - Article
AN - SCOPUS:85122938969
SN - 0944-2669
VL - 61
SP - 1
EP - 20
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
M1 - 40
ER -