Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions
Analysis of PDEs
2017-03-02 v2
Abstract
Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the construction of Spradlin and Tamasan [ST14] on the disc.
Keywords
Cite
@article{arxiv.1510.05081,
title = {Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions},
author = {Mickael Dos Santos},
journal= {arXiv preprint arXiv:1510.05081},
year = {2017}
}