Search results for "Functions with bounded variation"

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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
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Fine properties of functions with bounded variation in Carnot-Carathéodory spaces

2019

Abstract We study properties of functions with bounded variation in Carnot-Caratheodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R , we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.

Pure mathematicsApplied Mathematics010102 general mathematicsvariaatiolaskentaCarnot-Carathéodory spaces; Functions with bounded variationType (model theory)Classification of discontinuitiesSpace (mathematics)01 natural sciencesdifferentiaaligeometria010101 applied mathematicsDiscontinuity (linguistics)Functions with bounded variationBounded variationCarnot-Carathéodory spacesJumpAlmost everywheremittateoriaDifferentiable function0101 mathematicsfunctions with bounded variationfunktiotAnalysisMathematicsJournal of Mathematical Analysis and Applications
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