24 citations · 26 across the 10 of their papers we have counts for
10 papers
Mosco convergence framework for singular limits of gradient flows on Hilbert spaces with applications
Yoshikazu Giga, Michał Łasica, Piotr Rybka
We consider the question of convergence of a sequence of gradient flows defined on different Hilbert spaces. In order to give meaning to this idea, we introduce a notion of connect…
Adaptive double-phase Rudin--Osher--Fatemi denoising model
Wojciech Górny, Michał Łasica, Alexandros Matsoukas
Even though more than 30 years have passed since the seminal Rudin--Osher--Fatemi (ROF) paper on total variation (TV) denoising, it remains relevant due to its simplicity, robustne…
Euler-Lagrange equations for variable-growth total variation
Wojciech Górny, Michał Łasica, Alexandros Matsoukas
We consider a class of integral functionals with Musielak-Orlicz type variable growth, possibly linear in some regions of the domain. This includes power-type integrands wit…
A few topics on total variation flows
Yoshikazu Giga, Hirotoshi Kuroda, Michał Łasica
Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including defini…
The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary
Yoshikazu Giga, Michał Łasica, Piotr Rybka
We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the la…
Local estimates for vectorial Rudin-Osher-Fatemi type problems in one dimension
Zofia Grochulska, Michał Łasica
We consider the Rudin-Osher-Fatemi variational denoising model with general regularizing term in one-dimensional, vector-valued setting. We obtain local estimates on the singular p…
Existence of solutions to a class of variational problems with linear growth on convex domains
Michał Łasica, Piotr Rybka
We consider a class of convex integral functionals composed of a term of linear growth in the gradient of the argument, and a fidelity term involving distance from a datum. S…
Total variation denoising in anisotropy
Michał Łasica, Salvador Moll, Piotr B. Mucha
We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underly…
Analysis of solutions to a model parabolic equation with very singular diffusion
Michał Łasica
We consider a singular parabolic equation of form \[ u_t = u_{xx} + \fracα{2}(\mathrm{sgn}\,u_x)_x \] with periodic boundary conditions. Solutions to this kind of equations exhibit…
On steady solutions to vacuumless Newtonian models of compressible flow
Michał Łasica
We prove the existence of weak solutions to the steady compressible Navier-Stokes system in the barotropic case for a class of pressure laws singular at vacuum. We consider the pro…