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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46E35, 47B38

Retrieve articles in all journals with MSC (2000): 46E35, 47B38

Additional Information

Markus Biegert
Affiliation: Institute of Applied Analysis, University of Ulm, 89069 Ulm, Germany

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.