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

 

The complex Hessian equation with infinite Dirichlet boundary value


Authors: Ni Xiang and Xiao-Ping Yang
Journal: Proc. Amer. Math. Soc. 136 (2008), 2103-2111
MSC (2000): Primary 32A05, 35J60
Published electronically: February 18, 2008
MathSciNet review: 2383516
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Abstract: The existence and nonexistence of the $ \Gamma$-subharmonic solutions for the complex Hessian equations with infinite Dirichlet boundary value are proved in the certain bounded domain in $ C^n$. We calculate the k-Hessian of the radially symmetric function and use radial functions to construct various barrier functions in this paper. Moreover, it is shown that the growth rate conditions are nearly optimal.


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Additional Information

Ni Xiang
Affiliation: School of Science, Nanjing University of Science & Technology, Nanjing, People’s Republic of China 210094
Email: nixiang_810715@yahoo.com.cn

Xiao-Ping Yang
Affiliation: School of Science, Nanjing University of Science & Technology, Nanjing, People’s Republic of China 210094
Email: xpyang@mail.njust.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09354-4
PII: S 0002-9939(08)09354-4
Keywords: Complex Hessian equation, infinite boundary value, $\Gamma$-subharmonic
Received by editor(s): March 21, 2007
Published electronically: February 18, 2008
Additional Notes: The first author was supported in part by the National Natural Science Foundation of Jiangsu Province #BK2006209.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.