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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On traces of Sobolev functions on the boundary of extension domains


Author: Markus Biegert
Journal: Proc. Amer. Math. Soc. 137 (2009), 4169-4176
MSC (2000): Primary 46E35, 47B38
Published electronically: July 21, 2009
MathSciNet review: 2538577
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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]$.


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Additional Information

Markus Biegert
Affiliation: Institute of Applied Analysis, University of Ulm, 89069 Ulm, Germany
Email: markus.biegert@uni-ulm.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10045-X
PII: S 0002-9939(09)10045-X
Keywords: Sobolev spaces, traces, Sobolev extension domains
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.