Traces of functions of L1/2 Dirichlet spaces on the Carathéodory boundary

Vladimir Gol'Dshtein; Alexander Ukhlov

doi:10.4064/sm8485-8-2016

Traces of functions of L1/2 Dirichlet spaces on the Carathéodory boundary

Vladimir Gol'Dshtein
, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that any weakly differentiable function with a square integrable gradient can be extended to the Carathéodory boundary of any simply connected planar domain Ω = R² up to a set of conformal capacity zero. This result is based on the notion of capacitary boundary associated with the Dirichlet space L1/2(Ω).

Original language	English
Pages (from-to)	209-224
Number of pages	16
Journal	Studia Mathematica
Volume	235
Issue number	3
DOIs	https://doi.org/10.4064/sm8485-8-2016
State	Published - 1 Jan 2016

Keywords

Conformal mappings
Sobolev spaces

ASJC Scopus subject areas

General Mathematics

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10.4064/sm8485-8-2016

Cite this

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title = "Traces of functions of L1/2 Dirichlet spaces on the Carath{\'e}odory boundary",

abstract = "We prove that any weakly differentiable function with a square integrable gradient can be extended to the Carath{\'e}odory boundary of any simply connected planar domain Ω = R2 up to a set of conformal capacity zero. This result is based on the notion of capacitary boundary associated with the Dirichlet space L1/2(Ω).",

keywords = "Conformal mappings, Sobolev spaces",

author = "Vladimir Gol'Dshtein and Alexander Ukhlov",

note = "Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2016.",

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AU - Ukhlov, Alexander

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N2 - We prove that any weakly differentiable function with a square integrable gradient can be extended to the Carathéodory boundary of any simply connected planar domain Ω = R2 up to a set of conformal capacity zero. This result is based on the notion of capacitary boundary associated with the Dirichlet space L1/2(Ω).

AB - We prove that any weakly differentiable function with a square integrable gradient can be extended to the Carathéodory boundary of any simply connected planar domain Ω = R2 up to a set of conformal capacity zero. This result is based on the notion of capacitary boundary associated with the Dirichlet space L1/2(Ω).

KW - Conformal mappings

KW - Sobolev spaces

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U2 - 10.4064/sm8485-8-2016

DO - 10.4064/sm8485-8-2016

M3 - Article

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VL - 235

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JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

Traces of functions of L1/2 Dirichlet spaces on the Carathéodory boundary

Abstract

Keywords

ASJC Scopus subject areas

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