On indecomposable sets with applications
Mathematics Department, University of Cincinnati, 2600 Clifton Ave.
Cincinnati OH 45221.
Revised: 29 October 2013
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.
Mathematics Subject Classification: 28A75
Key words: Sets of finite perimeter / indecomposable sets
© EDP Sciences, SMAI, 2014