Inserted: 29 oct 2010
Last Updated: 1 mar 2014
Journal: International Mathematical Series (N.Y.)
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.