On indecomposable sets with applications
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 612-631.

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.

DOI : 10.1051/cocv/2013077
Classification : 28A75
Mots-clés : sets of finite perimeter, indecomposable sets 
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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. http://www.numdam.org/articles/10.1051/cocv/2013077/

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