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

 

Necessary and sufficient conditions on solvability for Hessian inequalities


Authors: Xiaohu Ji and Jiguang Bao
Journal: Proc. Amer. Math. Soc. 138 (2010), 175-188
MSC (2000): Primary 35J60, 35J85
Published electronically: September 3, 2009
MathSciNet review: 2550182
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Abstract: In this paper, we discuss the solvability of the Hessian inequality $ \sigma^{\frac{1}{k}}_{k}(\lambda (D^{2}u)) \ge f(u)$ on the entire space $ \mathbb{R}^{n}$ and provide a necessary and sufficient condition, which can be regarded as a generalized Keller-Osserman condition.


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Additional Information

Xiaohu Ji
Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China
Email: Ji.Xiaohu@hotmail.com

Jiguang Bao
Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China
Email: jgbao@bnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10032-1
PII: S 0002-9939(09)10032-1
Keywords: Hessian equation, subsolution, existence, nonexistence, Keller-Osserman condition
Received by editor(s): February 20, 2009
Published electronically: September 3, 2009
Additional Notes: This work was supported by the National Natural Science Foundation of China (10671022) and the Doctoral Programme Foundation of the Institute of Higher Education of China (20060027023).
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.