Zero volume boundary for extension domains from Sobolev to BV

2022/05/22 by Tapio Rajala, Zheng Zhu, Rajala, Tapio +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2205.10801

openalex publication_date 2022/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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∈∂\boz. Especially, the boundary of any planar (W^{1, p}, BV)-extension domain is of volume zero.

Related

• The volume of the boundary of a Sobolev (p,q)-extension domain II
• The volume of the boundary of a Sobolev (p,q)-extension domain
• Dimension estimates for the boundary of planar Sobolev extension domains
• Strong BV-extension and W^1,1-extension domains
• Dimension estimate for the two-sided points of planar Sobolev extension domains