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A note on the support of a Sobolev function on a $k$-cell

Author(s): W. K. Ziemer
Journal: Proc. Amer. Math. Soc. 132 (2004), 1987-1995.
MSC (2000): Primary 46E35
Posted: December 19, 2003
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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 $(k+1)/2$.

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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

DOI: 10.1090/S0002-9939-03-07335-0
PII: S 0002-9939(03)07335-0
Received by editor(s): May 3, 2001
Received by editor(s) in revised form: March 11, 2003
Posted: December 19, 2003
Communicated by: David Preiss
Copyright of article: Copyright 2003, American Mathematical Society

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