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Existence of solutions with asymptotic behavior of exterior problems of Hessian equations


Author: Limei Dai
Journal: Proc. Amer. Math. Soc. 139 (2011), 2853-2861
MSC (2010): Primary 35J96, 35J60
DOI: https://doi.org/10.1090/S0002-9939-2011-10833-5
Published electronically: January 28, 2011
MathSciNet review: 2801627
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we use the Perron method to prove the existence of viscosity solutions with asymptotic behavior at infinity to Hessian equations.


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  • [1] L. Caffarelli, Y. Y. Li, An extension to a theorem of Jörgens, Calabi, and Pogorelov, Comm. Pure Appl. Math. 56 (2003) 549-583. MR 1953651 (2004c:35116)
  • [2] L. Caffarelli, Y. Y. Li, Some multi-valued solutions to Monge-Ampère equations, Comm. Anal. Geom. 14 (2006) 411-441. MR 2260718 (2007i:35067)
  • [3] L. Caffarelli, L. Nirenberg, J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian, Acta Math. 155 (1985) 261-301. MR 806416 (87f:35098)
  • [4] A. Colesanti, P. Salani, Hessian equations in non-smooth domains, Nonlinear Anal. 38 (1999) 803-812. MR 1710156 (2001i:35088)
  • [5] K. S. Chou, X. J. Wang, A variational theory of the Hessian equation, Comm. Pure Appl. Math. 54 (2001) 1029-1064. MR 1835381 (2002e:35072)
  • [6] B. Guan, The Dirichlet problem for a class of fully nonlinear elliptic equations, Comm. Partial Differential Equations 19 (1994) 399-416. MR 1265805 (95c:35100)
  • [7] H. Ishii, P. L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1990) 26-78. MR 1031377 (90m:35015)
  • [8] N. S. Trudinger, On the Dirichlet problem for Hessian equations, Acta Math. 175 (1995) 151-164. MR 1368245 (96m:35113)
  • [9] N. S. Trudinger, Weak solutions of Hessian equations (English summary), Comm. Partial Differential Equations 22 (1997) 1251-1261. MR 1466315 (99a:35077)
  • [10] N. S. Trudinger, X. J. Wang, Hessian measures. II, Ann. of Math. (2) 150 (1999) 579-604. MR 1726702 (2001f:35141)
  • [11] J. I. E. Urbas, On the existence of nonclassical solutions for two classes of fully nonlinear elliptic equations, Indiana Univ. Math. J. 39 (1990) 355-382. MR 1089043 (92h:35074)

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Additional Information

Limei Dai
Affiliation: School of Mathematics and Information Science, Weifang University, Shandong 261061, People’s Republic of China
Email: limeidai@yahoo.com.cn

DOI: https://doi.org/10.1090/S0002-9939-2011-10833-5
Keywords: Hessian equations, viscosity solutions, asymptotic behavior.
Received by editor(s): May 5, 2010
Received by editor(s) in revised form: July 28, 2010
Published electronically: January 28, 2011
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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