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On indecomposable sets with applications

Published online by Cambridge University Press:  28 March 2014

Andrew Lorent
Andrew Lorent*
Affiliation:
Mathematics Department, University of Cincinnati, 2600 Clifton Ave. Cincinnati OH 45221.. lorentaw@uc.edu

Abstract

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In this note we show the characteristic function of every indecomposable setF in theplane is BVequivalent to the characteristic function a closed set \hbox{See Formula in PDF} .We show by example this is false in dimension three and above. As a corollary to thisresult we show that for every ϵ > 0 a set of finite perimeter S can be approximated by aclosed subset \hbox{See Formula in PDF} with finitely many indecomposablecomponents and with the property that \hbox{See Formula in PDF} and \hbox{See Formula in PDF} .We apply this corollary to give a short proof that locally quasiminimizing sets in theplane are BVlextension domains.

Keywords

Sets of finite perimeterindecomposable sets

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014, pp. 612 - 631
Copyright
© EDP Sciences, SMAI, 2014

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