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math.AP2024
On the Dirichlet problem for the one-dimensional ROF functional
Piotr Rybka
We provide a number of sufficient conditions for that minimizers of the one-dimensional Rudin-Osher-Fatemi functional satisfy the Dirichlet data in the trace sense. For this purpos…
math.AP2024
The non-convex planar Least Gradient Problem
Samer Dweik, Piotr Rybka, Ahmad Sabra
We study the least gradient problem in bounded regions with Lipschitz boundary in the plane. We provide a set of conditions for the existence of solutions in non-convex simply conn…