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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
DOI: https://doi.org/10.1090/S0002-9939-09-10045-X
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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  • 1. David R. Adams and Lars Inge Hedberg, Function spaces and potential theory, Grundlehren der mathematischen Wissenschaften, vol. 314, Springer-Verlag, Berlin, 1996. MR 97j:46024
  • 2. Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, vol. 65, Academic Press, New York, 1975. MR 56:9247
  • 3. Wolfgang Arendt and Mahamadi Warma, The Laplacian with Robin boundary conditions on arbitrary domains, Potential Anal. 19 (2003), no. 4, 341-363. MR 1988110
  • 4. Markus Biegert, Elliptic problems on varying domains, Dissertation, Logos Verlag, Berlin, 2005.
  • 5. -, The relative capacity, Ulmer Seminare 14 (2009), 25-41.
  • 6. -, On a capacity for modular spaces, Journal of Mathematical Analysis and Applications 358 (2009), no. 2, 294-306.
  • 7. Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu, Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces, Mem. Amer. Math. Soc. 182 (2006), no. 857. MR 2229731 (2008h:43016)
  • 8. Piotr Hajłasz and Olli Martio, Traces of Sobolev functions on fractal type sets and characterization of extension domains, J. Funct. Anal. 143 (1997), no. 1, 221-246. MR 1428124 (98d:46034)
  • 9. Petteri Harjulehto, Traces and Sobolev extension domains, Proc. Amer. Math. Soc. 134 (2006), no. 8, 2373-2382 (electronic). MR 2213711 (2007a:46032)
  • 10. A. Jonsson, The trace of potentials on general sets, Ark. Mat. 17 (1979), no. 1, 1-18. MR 0543499 (80i:46029)
  • 11. Vladimir G. Maz'ya, Sobolev spaces, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1985, translated from the Russian by T. O. Shaposhnikova. MR 87g:46056
  • 12. Hans Wallin, The trace to the boundary of Sobolev spaces on a snowflake, Manuscripta Math. 73 (1991), no. 2, 117-125. MR 1128682 (92k:46053)

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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: https://doi.org/10.1090/S0002-9939-09-10045-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.

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