On traces of Sobolev functions on the boundary of extension domains
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- by Markus Biegert
- Proc. Amer. Math. Soc. 137 (2009), 4169-4176
- DOI: https://doi.org/10.1090/S0002-9939-09-10045-X
- Published electronically: July 21, 2009
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Abstract:
Assume that $\Omega \subset \mathbb {R}^N$ is a bounded $W^{1,p}$-extension domain and that $\mu$ is an upper $d$-Ahlfors measure on $\partial \Omega$ with $p\in (1,N)$ and $d\in (N-p,N)$. Then there exist continuous trace operators from $W^{1,p}(\Omega )$ into $L^q(\partial \Omega ,d\mu )$ and into $B^p_\beta (\partial \Omega ,d\mu )$ for every $q\in [1,dp/(N-p)]$ and every $\beta \in (0,1-(N-d)/p]$.References
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Bibliographic Information
- Markus Biegert
- Affiliation: Institute of Applied Analysis, University of Ulm, 89069 Ulm, Germany
- Email: markus.biegert@uni-ulm.de
- Received by editor(s): March 30, 2009
- Received by editor(s) in revised form: April 1, 2009
- Published electronically: July 21, 2009
- Communicated by: Nigel J. Kalton
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4169-4176
- MSC (2000): Primary 46E35, 47B38
- DOI: https://doi.org/10.1090/S0002-9939-09-10045-X
- MathSciNet review: 2538577