Year: 2014
Type: article
Abstract: In this note we show the characteristic function of every indecomposable set F in the plane is BV equivalent to the characteristic function a closed set . We show by example this is false in dimension three and above. As a corollary to this result we show that for every ϵ > 0 a set of finite perimeter S can be approximated by a closed subset with finitely many indecomposable components and with the property that and . We apply this corollary to give a short proof that locally quasiminimizing sets in the plane are BVl extension domains.
DOI: 10.1051/cocv/2013077
Author: Andrew Lorent
Institution: University of Cincinnati
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2086498086