Necessary and sufficient conditions on solvability for Hessian inequalities
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- by Xiaohu Ji and Jiguang Bao PDF
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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.References
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 175-188
- MSC (2000): Primary 35J60, 35J85
- DOI: https://doi.org/10.1090/S0002-9939-09-10032-1
- MathSciNet review: 2550182