Zero volume boundary for extension domains from Sobolev to $BV$
Analysis of PDEs
2022-05-24 v1 Functional Analysis
Abstract
In this note, we prove that the boundary of a -extension domain is of volume zero under the assumption that the domain is -fat at almost every . Especially, the boundary of any planar -extension domain is of volume zero.
Cite
@article{arxiv.2205.10801,
title = {Zero volume boundary for extension domains from Sobolev to $BV$},
author = {Tapio Rajala and Zheng Zhu},
journal= {arXiv preprint arXiv:2205.10801},
year = {2022}
}