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

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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 languageEnglish
Pages (from-to)209-224
Number of pages16
JournalStudia Mathematica
Volume235
Issue number3
DOIs
StatePublished - 1 Jan 2016

Keywords

  • Conformal mappings
  • Sobolev spaces

ASJC Scopus subject areas

  • Mathematics (all)

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