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Traces and Sobolev extension domains


Author: Petteri Harjulehto
Journal: Proc. Amer. Math. Soc. 134 (2006), 2373-2382
MSC (2000): Primary 46E35
DOI: https://doi.org/10.1090/S0002-9939-06-08228-1
Published electronically: February 8, 2006
MathSciNet review: 2213711
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Abstract: Assume that $ \Omega \subset{\mathbb{R}^n}$ is a bounded domain and its boundary $ \partial \Omega$ is $ m$-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.


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Additional Information

Petteri Harjulehto
Affiliation: Department of Mathematics and Statistics, P.O. Box 68 (Gustav Hällströmin katu 2B), FIN-00014 University of Helsinki, Finland
Email: petteri.harjulehto@helsinki.fi

DOI: https://doi.org/10.1090/S0002-9939-06-08228-1
Keywords: Sobolev space, Besov space, trace operator, extension operator
Received by editor(s): October 26, 2000
Received by editor(s) in revised form: March 10, 2005
Published electronically: February 8, 2006
Communicated by: David Preiss
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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