English

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 (W1,p,BV)(W^{1, p}, BV)-extension domain is of volume zero under the assumption that the domain \boz\boz is 11-fat at almost every x\bozx\in\partial\boz. Especially, the boundary of any planar (W1,p,BV)(W^{1, p}, BV)-extension domain is of volume zero.

Keywords

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}
}