A note on the support of a Sobolev function on a $k$-cell
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- by W. K. Ziemer PDF
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Abstract:
It is shown that a $k$-cell (the homeomorphic image of a closed ball in $\mathbb {R}^{k}$) in $\mathbb {R}^{n}$, $1\leq k<n$, cannot support a function in $W^{1,p}(\mathbb {R}^{n})$ if $p>[\frac {k+1}{2}]$, the greatest integer in $(k+1)/2$.References
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Additional Information
- W. K. Ziemer
- Affiliation: Department of Mathematics, California State University Long Beach, Long Beach, California 90840-1001
- Email: wziemer@csulb.edu
- Received by editor(s): May 3, 2001
- Received by editor(s) in revised form: March 11, 2003
- Published electronically: December 19, 2003
- Communicated by: David Preiss
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1987-1995
- MSC (2000): Primary 46E35
- DOI: https://doi.org/10.1090/S0002-9939-03-07335-0
- MathSciNet review: 2053970