Special cases of the planar least gradient problem
Analysis of PDEs
2016-05-23 v2
Abstract
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, we impose the Dirichlet data on the boundary of a rectangle, an example of convex but not strictly convex domain. We show the existence of solutions and study their properties for particular cases of data.
Cite
@article{arxiv.1605.00035,
title = {Special cases of the planar least gradient problem},
author = {Wojciech Górny and Piotr Rybka and Ahmad Sabra},
journal= {arXiv preprint arXiv:1605.00035},
year = {2016}
}