Variational solutions to the total variation flow on metric measure spaces Article Swipe
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Bounded variation
Mathematics
Measure (data warehouse)
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Metric (unit)
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Bounded function
Flow (mathematics)
Mathematical analysis
Pure mathematics
Geometry
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Vito Buffa
,
Juha Kinnunen
,
Cintia Pacchiano Camacho
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.11908
· OA: W4286962316
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.11908
· OA: W4286962316
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.
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