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–Maz’ya [BM] 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.

Geometric Properties of Planar BV Extension Domains

MIRANDA, Michele;
2010

Abstract

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–Maz’ya [BM] 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.
2010
9781441913463
Extension domains; Sobolev spaces; Functions with bounded variation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1401210
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