On Sobolev extension domains in $R^n$

Abstract

We describe a class of Sobolev $W_p^k$-extension domains $\Omega \subset R^n$ determined by a certain inner subhyperbolic metric in $\Omega$. This enables us to characterize finitely connected Sobolev $W_p^1$-extension domains in $R^2$ for each $p>2$.

37 pages

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