Strong approximation of sets of finite perimeter in metric spaces

In the setting of a metric space equipped with a doubling measure that supports a Poincaré inequality, we show that any set of finite perimeter can be approximated in the BV norm by a set whose topological and measure theoretic boundaries almost coincide. The proof relies on a quasicontinuity-type r...

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Veröffentlicht in:	Manuscripta mathematica 2018-03, Vol.155 (3-4), p.503-522
1. Verfasser:	Lahti, Panu
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebraic Geometry Calculus of Variations and Optimal Control Optimization Geometry Lie Groups Mathematics Mathematics and Statistics Metric space Number Theory Topological Groups
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description	In the setting of a metric space equipped with a doubling measure that supports a Poincaré inequality, we show that any set of finite perimeter can be approximated in the BV norm by a set whose topological and measure theoretic boundaries almost coincide. The proof relies on a quasicontinuity-type result for BV functions proved by Lahti and Shanmugalingam (J Math Pures Appl 107(2): 150–182, 2017 ).
doi_str_mv	10.1007/s00229-017-0948-1
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subjects	Algebraic Geometry Calculus of Variations and Optimal Control Optimization Geometry Lie Groups Mathematics Mathematics and Statistics Metric space Number Theory Topological Groups
title	Strong approximation of sets of finite perimeter in metric spaces
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