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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 See Formula in PDF \hbox{See Formula in PDF} . 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 See Formula in PDF \hbox{See Formula in PDF} with finitely many indecomposable components and with the property that See Formula in PDF \hbox{See Formula in PDF} and See Formula in PDF \hbox{See Formula in PDF} . We apply this corollary to give a short proof that locally quasiminimizing sets in the plane are BVl extension domains.
@article{COCV_2014__20_2_612_0,
author = {Lorent, Andrew},
title = {On indecomposable sets with applications},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {612--631},
publisher = {EDP-Sciences},
volume = {20},
number = {2},
year = {2014},
doi = {10.1051/cocv/2013077},
mrnumber = {3264218},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013077/}
}
TY - JOUR AU - Lorent, Andrew TI - On indecomposable sets with applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 612 EP - 631 VL - 20 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013077/ DO - 10.1051/cocv/2013077 LA - en ID - COCV_2014__20_2_612_0 ER -
%0 Journal Article %A Lorent, Andrew %T On indecomposable sets with applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 612-631 %V 20 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013077/ %R 10.1051/cocv/2013077 %G en %F COCV_2014__20_2_612_0
Lorent, Andrew. On indecomposable sets with applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 612-631. doi: 10.1051/cocv/2013077
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