# On indecomposable sets with applications

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 2, page 612-631
- ISSN: 1292-8119

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topLorent, Andrew. "On indecomposable sets with applications." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 612-631. <http://eudml.org/doc/272893>.

@article{Lorent2014,

abstract = {In this note we show the characteristic function of every indecomposable set F in the plane is BVequivalent to the characteristic function a closed set See Formula in PDF 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 everyϵ > 0 a set of finite perimeter Scan be approximated by a closed subset See Formula in PDF See Formula in PDF with finitely many indecomposable components and with the property that See Formula in PDF See Formula in PDF and See Formula in PDF See Formula in PDF . We apply this corollary to give a short proof that locally quasiminimizing sets in the plane areBVl extension domains.},

author = {Lorent, Andrew},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {sets of finite perimeter; indecomposable sets},

language = {eng},

number = {2},

pages = {612-631},

publisher = {EDP-Sciences},

title = {On indecomposable sets with applications},

url = {http://eudml.org/doc/272893},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Lorent, Andrew

TI - On indecomposable sets with applications

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 2

SP - 612

EP - 631

AB - In this note we show the characteristic function of every indecomposable set F in the plane is BVequivalent to the characteristic function a closed set See Formula in PDF 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 everyϵ > 0 a set of finite perimeter Scan be approximated by a closed subset See Formula in PDF See Formula in PDF with finitely many indecomposable components and with the property that See Formula in PDF See Formula in PDF and See Formula in PDF See Formula in PDF . We apply this corollary to give a short proof that locally quasiminimizing sets in the plane areBVl extension domains.

LA - eng

KW - sets of finite perimeter; indecomposable sets

UR - http://eudml.org/doc/272893

ER -

## References

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