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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
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Abstract

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.

Keywords

Sets of finite perimeterindecomposable sets
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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