6533b7d8fe1ef96bd126a48f

RESEARCH PRODUCT

Geometric Properties of Planar BV -Extension Domains

Nageswari ShanmugalingamMichele MirandaPekka Koskela

subject

Discrete mathematicsQuasiconformal mappingMathematics::Analysis of PDEsGeometric propertySobolev spaceQuasiconvex functionExtension domains; Sobolev spaces; Functions with bounded variationPlanarSobolev spacesFunctions with bounded variationBounded functionSimply connected spaceInvariant (mathematics)Extension domainsMathematics

description

We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.

yearjournalcountryeditionlanguage
2009-11-18
https://doi.org/10.1007/978-1-4419-1341-8_11