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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the exterior Dirichlet problem for Hessian equations


Authors: Jiguang Bao, Haigang Li and Yanyan Li
Journal: Trans. Amer. Math. Soc. 366 (2014), 6183-6200
MSC (2010): Primary 35J60, 35J67
Published electronically: June 16, 2014
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Abstract: In this paper, we establish a theorem on the existence of the solutions of the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity. This extends a result of Caffarelli and Li (2003) for the Monge-Ampère equation to Hessian equations.


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Additional Information

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

Haigang Li
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: hgli@bnu.edu.cn

Yanyan Li
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854
Email: yyli@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05867-4
PII: S 0002-9947(2014)05867-4
Received by editor(s): April 12, 2012
Published electronically: June 16, 2014
Additional Notes: The second author was the corresponding author
Article copyright: © Copyright 2014 American Mathematical Society