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.File in questo prodotto:
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