On Sobolev extension domains in Rn

We describe a class of Sobolev Wkp -extension domains Ω ⊂ Rn determined by a certain inner subhyperbolic metric in Ω. This enables us to characterize finitely connected Sobolev W1 p-extension domains in R2 for each p >2. © 2010 Elsevier Inc. All rights reserved