Search results for "quasidisks"

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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
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Sobolev homeomorphic extensions onto John domains

2020

Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous $W^{1,2}$-extension but not even a homeomorphic $W^{1,1}$-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents $p<2$. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.

funktioteoriaMathematics::Dynamical SystemsSobolev extensionsMathematics - Complex Variables46E35 58E20quasidisksFOS: MathematicsMathematics::General TopologySobolev homeomorphismsComplex Variables (math.CV)John domainsfunktionaalianalyysiMathematics::Geometric Topology
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