Calculus of Variations and Geometric Measure Theory

P. Koskela - M. Miranda Jr - N. Shanmugalingam

Geometric properties of planar BV-extension domains

created by shanmugal on 29 Oct 2010
modified by paolini on 01 Mar 2014


Published Paper

Inserted: 29 oct 2010
Last Updated: 1 mar 2014

Journal: International Mathematical Series (N.Y.)
Volume: 11
Number: 1
Pages: 255-272
Year: 2010


In this paper we investigate geometric properties of planar domains that are extension for functions with bounded variation. We start from a characterization of such domains given by Burago--Mazya and prove that a bounded simply connected domain is a BV extension domain if and only if its complement is quasiconvex. We also show some relations with Sobolev extension domains.