The total variation flow with time dependent boundary values

The total variation flow with time dependent boundary values

In this paper we consider the Cauchy–Dirichlet problem for the total variation flow on a space-time cylinder Ω T = Ω × ( 0 , T ) with a bounded Lipschitz domain Ω in R n , when the initial datum u o is in L 2 ( Ω ) and the time dependent lateral boundary values g are given by a function in L w ∗ 1 (...

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Veröffentlicht in:Calculus of variations and partial differential equations 2016-08, Vol.55 (4), p.1-31, Article 108
Hauptverfasser: Bögelein, Verena, Duzaar, Frank, Scheven, Christoph
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Cylinders
Dirichlet problem
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Time dependence
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Zusammenfassung:In this paper we consider the Cauchy–Dirichlet problem for the total variation flow on a space-time cylinder Ω T = Ω × ( 0 , T ) with a bounded Lipschitz domain Ω in R n , when the initial datum u o is in L 2 ( Ω ) and the time dependent lateral boundary values g are given by a function in L w ∗ 1 ( 0 , T ; BV ( Ω ) ) with time derivative ∂ t g ∈ L 2 ( Ω T ) .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-016-1041-4