3 papers
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…
math.DG2024
A classification of solitons for the surface diffusion flow of entire graphs
Piotr Rybka, Glen Wheeler
In this article we classify solitons (equilibria, self-similar solutions and travelling waves) for the surface diffusion flow of entire graphs of function over the real line.