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Necessary and sufficient conditions on existence and convexity of solutions for Dirichlet problems of Hessian equations on exterior domains


Authors: Chong Wang and Jiguang Bao
Journal: Proc. Amer. Math. Soc. 141 (2013), 1289-1296
MSC (2010): Primary 35J60; Secondary 35J96
DOI: https://doi.org/10.1090/S0002-9939-2012-11738-1
Published electronically: August 16, 2012
MathSciNet review: 3008876
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Abstract: In this paper, we are concerned with the Dirichlet problems of Hessian equations on exterior domains with prescribed asymptotic behavior at infinity, and we obtain the necessary and sufficient conditions on existence and convexity of radial solutions.


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Additional Information

Chong Wang
Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China

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

DOI: https://doi.org/10.1090/S0002-9939-2012-11738-1
Keywords: Hessian equation, necessary and sufficient condition, existence, convexity, asymptotic behavior, radial solution, exterior Dirichlet problem
Received by editor(s): August 5, 2011
Published electronically: August 16, 2012
Communicated by: James E. Colliander
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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