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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ L^p$ estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities


Author: Dimiter Vassilev
Journal: Trans. Amer. Math. Soc. 363 (2011), 37-62
MSC (2000): Primary 35J65, 35B05
Published electronically: August 31, 2010
MathSciNet review: 2719670
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Abstract: Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp $ L^q$ regularity for finite energy solutions of p-Laplace equations involving critical exponents and possible singularity on a sub-space of $ \mathbb{R}^n$, which imply asymptotic behavior of the solutions at infinity. In addition, we find the best constant and extremals in the case of the considered $ L^2$ Hardy-Sobolev inequality.


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Additional Information

Dimiter Vassilev
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131 – and – Department of Mathematics, University of California, Riverside, Riverside, California 92521
Email: vassilev@math.unm.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04850-0
PII: S 0002-9947(2010)04850-0
Received by editor(s): December 12, 2006
Received by editor(s) in revised form: April 25, 2008
Published electronically: August 31, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.