A Jordan domain whose hyperbolic metric is phi-integrable with integral of 1/phi finite admits Sobolev homeomorphic extensions for every boundary parametrization, and the condition is sharp.
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Homeomorphic Sobolev extensions and integrability of hyperbolic metric
A Jordan domain whose hyperbolic metric is phi-integrable with integral of 1/phi finite admits Sobolev homeomorphic extensions for every boundary parametrization, and the condition is sharp.