Zero volume boundary for extension domains from Sobolev to $BV$

Kavli Affiliate: Zheng Zhu

| First 5 Authors: Tapio Rajala, Zheng Zhu, , ,

| Summary:

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 $xinpartialboz$. Especially, the boundary of any planar
$(W^{1, p}, BV)$-extension domain is of volume zero.

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