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

 

Uniqueness for boundary blow-up problems with continuous weights


Author: Jorge García-Melián
Journal: Proc. Amer. Math. Soc. 135 (2007), 2785-2793
MSC (2000): Primary 35J25; Secondary 35J60
Published electronically: March 30, 2007
MathSciNet review: 2317953
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Abstract: In this paper, we prove that for $ p>1$ the problem $ \Delta u=a(x)u^p$ in a bounded $ C^2$ domain $ \Omega$ of $ \mathbb{R}^N$ has a unique positive solution with $ u=\infty$ on $ \partial\Omega$. The nonnegative weight $ a(x)$ is continuous in $ \overline{\Omega}$, but is only assumed to verify a ``bounded oscillations" condition of local nature near $ \partial\Omega$, in contrast with previous works, where a definite behavior of $ a$ near $ \partial\Omega$ was imposed.


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Additional Information

Jorge García-Melián
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, C/ Astrofísico Francisco Sánchez s/n, 38271, La Laguna, Spain
Email: jjgarmel@ull.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08822-3
PII: S 0002-9939(07)08822-3
Received by editor(s): May 8, 2006
Published electronically: March 30, 2007
Additional Notes: Supported by MEC and FEDER under grant MTM2005-06480.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.