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Proceedings of the American Mathematical Society

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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

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.