TY - JOUR
T1 - Variational solutions to the total variation flow on metric measure spaces
AU - Buffa, Vito
AU - Kinnunen, Juha
AU - Pacchiano Camacho, Cintia
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/7
Y1 - 2022/7
N2 - We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincaré inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and functions of bounded variation to prove a necessary and sufficient condition for a variational solution to be continuous at a given point.
AB - We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincaré inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and functions of bounded variation to prove a necessary and sufficient condition for a variational solution to be continuous at a given point.
KW - Metric measure spaces
KW - Parabolic Sobolev spaces
KW - Parabolic variational problems
KW - Sobolev spaces
KW - Time mollifications
UR - http://www.scopus.com/inward/record.url?scp=85126594296&partnerID=8YFLogxK
U2 - 10.1016/j.na.2022.112859
DO - 10.1016/j.na.2022.112859
M3 - Article
AN - SCOPUS:85126594296
SN - 0362-546X
VL - 220
SP - 1
EP - 31
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 112859
ER -