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Traces and Sobolev extension domains

Authors:	Petteri Harjulehto

Institution:	Department of Mathematics and Statistics, P.O. Box 68 (Gustav Hällströmin katu 2B), FIN-00014 University of Helsinki, Finland

Abstract:	Assume that $\Omega \subset{\mathbb{R}^n}$ is a bounded domain and its boundary $\partial \Omega$ is -regular, $n-1 \le m <n$ . We show that if there exists a bounded trace operator $T:W^{1,p}(\Omega) \to B^{p}_{1-\alpha}(\partial\Omega)$ , $1<p<\infty$ and $\alpha = \tfrac{n-m}{p}$ , and $(1-\lambda)$ -Hölder continuous functions are dense in $W^{1,p}(\Omega)$ , $0\le \lambda < n-m$ , then the domain $\Omega$ is a $W^{1,p}$ -extension domain.

Keywords:	Sobolev space Besov space trace operator extension operator

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