Not all traces on the circle come from functions of least gradient in the disk
Analysis of PDEs
2013-11-07 v1
Abstract
We provide an example of an function on the circle, which cannot be the trace of a function of bounded variation of least gradient in the disk. This shows that in theorems on existence and uniqueness of solutions to the least gradient problem, proven by Sternberg, Williams and Ziemer and published in 1992-1993, the hypothesis that the boundary data is continuous cannot be removed.
Keywords
Cite
@article{arxiv.1311.1494,
title = {Not all traces on the circle come from functions of least gradient in the disk},
author = {Greg Spradlin and Alexandru Tamasan},
journal= {arXiv preprint arXiv:1311.1494},
year = {2013}
}
Comments
15 pages, 3 figures