The Dirichlet Problem for the Total Variation Flow

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Regularity for solutions of the total variation denoising problem (2011, background): “] (see also [4] for the required adaptations to deal with the boundary condition), which deals with the case Ω = R .”
LOCAL SOLVABILITY OF A CONSTRAINED GRADIENT SYSTEM OF TOTAL VARIATION (2003, background): “, [6, 8] and also [13, 17, 19]), for a recent L1-theory, see [1, 2, 3, 7].”
Uniqueness of the Cheeger set of a convex body (2007, methodology): “Since |Dv | → ∞ uniformly in any subset of C at positive distance from C∗ (see the first lines of the proof of Lemma 3.1), this shows the uniform convergence of |z + ν | to 0 in such subsets.”
Variable Exponent, Linear Growth Functionals in Image Restoration (2006, background): “More related work on linear-growth functionals and their flows can be found in [2, 3, 4, 5, 6, 7, 12, 14, 33].”
Very singular diffusion equations: second and fourth order problems (2010, background): “However, its explicit characterization is often nontrivial [6] and it is well-studied for piecewise constant functions [ 3 ,4,45,87,95,96].”
On the behaviour of the solutions to p-Laplacian equations as p goes to 1 (2008, background): “2) have been studied by various authors (see for instance [4], [6], [9], [11], [12] and references there in).”