Abstract
Suppose that Ω is an open bounded domain with a Lipschitz boundary. The purpose of this chapter is to study the Dirichlet problem
where u0 ∈ L1(Ω) and ϕ ∈ L1 (∂Ω). This evolution equation is related to the gradient descent method used to solve the problem
where f ∈ L1(Ω), ϕ ∈ L∞ (∂Ω) (existence for this variational problem was proved in [118], Theorem 1.4).
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© 2004 Springer Basel AG
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Andreu-Vaillo, F., Mazón, J.M., Caselles, V. (2004). The Dirichlet Problem for the Total Variation Flow. In: Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Progress in Mathematics, vol 223. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7928-6_5
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DOI: https://doi.org/10.1007/978-3-0348-7928-6_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9624-5
Online ISBN: 978-3-0348-7928-6
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