Search results for "Extension domains"

showing 2 items of 2 documents

Geometric Properties of Planar BV -Extension Domains

2009

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.

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
researchProduct

Sobolev Extension on Lp-quasidisks

2021

AbstractIn this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.

Pure mathematicsSobolev extension domainsProperty (philosophy)Lp-quasidisksMathematics::Complex Variables010102 general mathematicsMathematics::Analysis of PDEs0102 computer and information sciencesExtension (predicate logic)01 natural sciencesPotential theoryfunktioteoriaSobolev spacehomeomorphism of finite distortion010201 computation theory & mathematics0101 mathematicsfunktionaalianalyysiAnalysisMathematicsPotential Analysis
researchProduct