Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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

 

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


Author: W. K. Ziemer
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1987-1995
MSC (2000): Primary 46E35
Published electronically: December 19, 2003
MathSciNet review: 2053970
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

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

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


Additional Information

W. K. Ziemer
Affiliation: Department of Mathematics, California State University Long Beach, Long Beach, California 90840-1001
Email: wziemer@csulb.edu

DOI: http://dx.doi.org/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
Published electronically: December 19, 2003
Communicated by: David Preiss
Article copyright: © Copyright 2003 American Mathematical Society