Search results for "Poisson extension"

showing 2 items of 2 documents

Weighted estimates for diffeomorphic extensions of homeomorphisms

2019

Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$

Pure mathematicsMathematics::Functional AnalysisMathematics - Complex VariablesdiffeomorphismGeneral MathematicsMultiple integralHigh Energy Physics::Phenomenologyinternal chord-arc domainPoisson extensionExtension (predicate logic)OmegafunktioteoriaHomeomorphism (graph theory)Domain (ring theory)FOS: MathematicsDiffeomorphismComplex Variables (math.CV)Mathematics
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Controlled diffeomorphic extension of homeomorphisms

2018

Let $\Omega$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$ be a homeomorphism. We show that $\varphi$ has finite dyadic energy if and only if $\varphi$ has a diffeomorphic extension $h: \mathbb D\rightarrow \Omega$ which has finite energy.

Mathematics::Functional AnalysisPure mathematicsMathematics::Dynamical SystemsMathematics - Complex VariablesdiffeomorphismApplied Mathematicsta111010102 general mathematicsHigh Energy Physics::PhenomenologyPoisson extensionExtension (predicate logic)01 natural sciencesHomeomorphismfunktioteoria010101 applied mathematicsDomain (ring theory)chord-arc curveFOS: MathematicsDiffeomorphismtopologia0101 mathematicsComplex Variables (math.CV)AnalysisEnergy (signal processing)Mathematics
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