| Issue |
ESAIM: COCV
Volume 20, Number 2, April-June 2014
|
|
|---|---|---|
| Page(s) | 612 - 631 | |
| DOI | https://doi.org/10.1051/cocv/2013077 | |
| Published online | 28 March 2014 | |
On indecomposable sets with applications
Mathematics Department, University of Cincinnati, 2600 Clifton Ave.
Cincinnati OH 45221.
lorentaw@uc.edu
Received:
14
May
2013
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
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