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 |
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Pages (from-to) | 209-224 |
Number of pages | 16 |
Journal | Studia Mathematica |
Volume | 235 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2016 |
Keywords
- Conformal mappings
- Sobolev spaces
ASJC Scopus subject areas
- General Mathematics