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

 

Hardy's inequality on exterior domains


Authors: J. Chabrowski and M. Willem
Journal: Proc. Amer. Math. Soc. 134 (2006), 1019-1022
MSC (2000): Primary 49R50, 35J70
Published electronically: October 28, 2005
MathSciNet review: 2196033
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Abstract: Let $ \Omega$ be a smooth exterior domain in $ \mathbb{R}^N$ and $ 1<p<{\infty}$. We prove that when $ p\neq N$, Hardy's $ L^p$ inequality is valid on $ \mathcal {D}^{1,p}_{0}(\Omega)$.


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Additional Information

J. Chabrowski
Affiliation: Department of Mathematics, University of Queensland, St. Lucia 4072, Queensland, Australia

M. Willem
Affiliation: Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08407-8
PII: S 0002-9939(05)08407-8
Keywords: Hardy's inequality, exterior domains, concentration at infinity, concentration at boundary.
Received by editor(s): December 24, 2003
Received by editor(s) in revised form: July 7, 2004
Published electronically: October 28, 2005
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society