Strong BV-extension and W-1,W-1-extension domains

摘要

We show that a bounded domain in a Euclidean space is a W-1,W-1-extension domain if and only if it is a strong BV-extension domain. In the planar case, bounded and strong BV -extension domains are shown to be exactly those BV -extension domains for which the set partial derivative Omega boolean OR(i) Omega(over line)(i) is purely 1-unrectifiable, where Omega(i) are the open connected components of R-2 Omega(over line).(c) 2022 The Author(s). Published by Elsevier Inc.