2 citations · 3 across the 10 of their papers we have counts for
17 papers
The trace space of anisotropic least gradient functions depends on the anisotropy
Wojciech Górny
We study the set of possible traces of anisotropic least gradient functions. We show that even on the unit disk it changes with the anisotropic norm: for two sufficiently regular s…
Optimal transport approach to Sobolev regularity of solutions to the weighted least gradient problem
Samer Dweik, Wojciech Górny
We study the equivalence between the weighted least gradient problem and the weighted Beckmann minimal flow problem or equivalently, the optimal transport problem with Riemannian c…
The double-bubble problem on the square lattice
Manuel Friedrich, Wojciech Górny, Ulisse Stefanelli
We investigate minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We…
The Neumann and Dirichlet problems for the total variation flow in metric measure spaces
Wojciech Górny, José M. Mazón
We study the Neumann and Dirichlet problems for the total variation flow in metric measure spaces. We prove existence and uniqueness of weak solutions and study their asymptotic be…
The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces
Wojciech Górny, José M. Mazón
In the framework of the first-order differential structure introduced by Gigli, we obtain a Gauss-Green formula on regular bounded open sets of metric measure spaces, valid for BV…
On the -Laplacian evolution equation in metric measure spaces
Wojciech Górny, José M. Mazón
The -Laplacian evolution equation in metric measure spaces has been studied as the gradient flow in of the -Cheeger energy (for ). In this paper, using…
Applications of optimal transport methods in the least gradient problem
Wojciech Górny
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship b…
Least gradient problem with Dirichlet condition imposed on a part of the boundary
Wojciech Górny
We provide an analysis of the least gradient problem in the case when the boundary datum is only imposed on a part of the boundary. First, we give a characterisation of solutions i…
Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents
Wojciech Górny
In the setting of metric measure spaces satisfying the doubling condition and the -Poincaré inequality, we prove a metric analogue of the Bourgain-Brezis-Mironescu formula f…
Local and nonlocal 1-Laplacian in Carnot groups
Wojciech Górny
We formulate and study the nonlocal and local least gradient problem, which is the Dirichlet problem for the 1-Laplace operator, in a quite natural setting of Carnot groups. We stu…
Least gradient functions in metric random walk spaces
Wojciech Górny, José M. Mazón
In this paper we study least gradient functions in metric random walk spaces, which include as particular cases the least gradient functions on locally finite weighted connected gr…
Least gradient problem on annuli
Samer Dweik, Wojciech Górny
We consider the two dimensional BV least gradient problem on an annulus with given boundary data . Firstly, we prove that this problem is equivalent to the opt…
regularity of least gradient functions
Wojciech Górny
It is shown that solutions to the anisotropic least gradient problem for boundary data lie in ; the exponent is shown to be optimal. M…
Existence of minimisers in the least gradient problem for general boundary data
Wojciech Górny
We study existence of minimisers to the least gradient problem on a strictly convex domain in two settings. On a bounded domain, we allow the boundary data to be discontinuous and…
Least gradient problem with respect to a non-strictly convex norm
Wojciech Górny
We study the planar least gradient problem with respect to an anisotropic norm for continuous boundary data. We prove existence of minimizers for strictly convex domains . F…
(Non)uniqueness of minimizers in the least gradient problem
Wojciech Górny
Minimizers in the least gradient problem with discontinuous boundary data need not be unique. However, all of them have a similar structure of level sets. Here, we give a full char…
Special cases of the planar least gradient problem
Wojciech Górny, Piotr Rybka, Ahmad Sabra
We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of the strictly convex domain. In the second case,…