Geodesic
Traces of functions of $L^1_2$ Dirichlet spaces on the Carathéodory boundary
Vladimir Gol’dshtein 1   ; Alexander Ukhlov 1
1 Department of Mathematics Ben-Gurion University of the Negev P.O. Box 653, Beer Sheva, 8410501, Israel
Studia Mathematica, Tome 235 (2016) no. 3, pp. 209-224 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\varOmega \not =\mathbb R^2$ up to a set of conformal capacity zero. This result is based on the notion of capacitary boundary associated with the Dirichlet space $L^1_2(\varOmega )$.
DOI : 10.4064/sm8485-8-2016
Keywords: prove weakly differentiable function square integrable gradient extended carath odory boundary simply connected planar domain varomega mathbb set conformal capacity zero result based notion capacitary boundary associated dirichlet space varomega

Vladimir Gol’dshtein  1   ; Alexander Ukhlov  1

1 Department of Mathematics Ben-Gurion University of the Negev P.O. Box 653, Beer Sheva, 8410501, Israel 
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Vladimir Gol’dshtein; Alexander Ukhlov. Traces of functions of $L^1_2$ Dirichlet spaces on the Carathéodory boundary. Studia Mathematica, Tome 235 (2016) no. 3, pp. 209-224. doi: 10.4064/sm8485-8-2016

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