Zero volume boundary for extension domains from Sobolev to $BV$
Tapio Rajala, Zheng Dong Zhu · arXiv (Cornell University) · 2022
In this note, we prove that the boundary of a $(W^{1, p}, BV)$-extension domain is of volume zero under the assumption that the domain $\boz$ is $1$-fat at almost every $x\in\partial\boz$. Especially, the boundary of any planar $(W^{1, p}, BV)$-extension domain is of volume zero.