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

 

A geometrical version of Hardy's inequality for $\stackrel{\circ}{\textrm{W}}{}^{1,p}(\Omega)$


Author: Jesper Tidblom
Journal: Proc. Amer. Math. Soc. 132 (2004), 2265-2271
MSC (2000): Primary 35P99; Secondary 35P20, 47A75, 47B25
Published electronically: March 25, 2004
MathSciNet review: 2052402
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Abstract: The aim of this article is to prove a Hardy-type inequality, concerning functions in $\stackrel{\circ}{\textrm{W}}{}^{1,p}(\Omega)$ for some domain $\Omega \subset R^n$, involving the volume of $\Omega$ and the distance to the boundary of $\Omega$. The inequality is a generalization of a recently proved inequality by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and A. Laptev (2002), which dealt with the special case $p=2$.


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Additional Information

Jesper Tidblom
Affiliation: Department of Mathematics, University of Stockholm, 106 91 Stockholm, Sweden
Email: jespert@math.su.se

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07526-4
PII: S 0002-9939(04)07526-4
Received by editor(s): January 28, 2002
Published electronically: March 25, 2004
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2004 American Mathematical Society