Planar least gradient problem: existence, regularity and anisotropic case
Analysis of PDEs
2017-09-29 v2
Abstract
We show existence of solutions to the least gradient problem on the plane for boundary data in . We also provide an example of a function , for which the solution exists. We also show non-uniqueness of solutions even for smooth boundary data in the anisotropic case for a nonsmooth anisotropy. We additionally prove a regularity result valid also in higher dimensions.
Cite
@article{arxiv.1608.02617,
title = {Planar least gradient problem: existence, regularity and anisotropic case},
author = {Wojciech Górny},
journal= {arXiv preprint arXiv:1608.02617},
year = {2017}
}