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

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- by Dimiter Vassilev
- Trans. Amer. Math. Soc.
**363**(2011), 37-62 - DOI: https://doi.org/10.1090/S0002-9947-2010-04850-0
- Published electronically: August 31, 2010
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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.## References

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## Bibliographic 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
- Received by editor(s): December 12, 2006
- Received by editor(s) in revised form: April 25, 2008
- Published electronically: August 31, 2010
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**363**(2011), 37-62 - MSC (2000): Primary 35J65, 35B05
- DOI: https://doi.org/10.1090/S0002-9947-2010-04850-0
- MathSciNet review: 2719670