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Hardy's inequality on exterior domains

Author(s): J. Chabrowski; M. Willem
Journal: Proc. Amer. Math. Soc. 134 (2006), 1019-1022.
MSC (2000): Primary 49R50, 35J70
Posted: October 28, 2005
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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 inequality is valid on $\mathcal {D}^{1,p}_{0}(\Omega)$ .

References:

1.: H. Brezis and M. Marcus, Hardy's inequality revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997) 217-237. MR 1655516 (99m:46075)
2.: F. Colin, Hardy's inequality in unbounded domains, Top. Meth. Nonlinear Anal. 17 (2001) 277-284. MR 1868901 (2002k:26030)
3.: M. Marcus, V. J. Mizel and Y. Pinchover, On the best constants for Hardy's inequality in ${\mathbb{R}}^N$ , Trans. Amer. Math. Soc. 350 (1998) 3237-3255. MR 1458330 (98k:26035)
4.: M. Marcus and I. Shafrir, An eigenvalue problem related to Hardy's inequality, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000) 581-604. MR 1817710 (2002c:49082)
5.: D. Smets, A concentration-compactness lemma with applications to singular eigenvalue problems, J. Funct. Anal. 167 (1999) 463-480. MR 1716204 (2002c:35202)

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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: 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
Posted: October 28, 2005
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2005, American Mathematical Society


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