On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains
Limei DAI, Jiguang BAO
On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains
In this paper, we obtain the uniqueness and existence of viscosity solutions with prescribed asymptotic behavior at infinity to Hessian equations in exterior domains.
Hessian equation / uniqueness / existence / viscosity solution / exterior domain
[1] |
Caffarelli L, Li Y Y. An extension to a theorem of Jörgens, Calabi, and Pogorelov. Communications on Pure and Applied Mathematics, 2003, 56: 549-583
CrossRef
Google scholar
|
[2] |
Caffarelli L, Li Y Y. Some multi-valued solutions to Monge-Ampère equations. Communications in Analysis and Geometry, 2006, 14: 411-441
|
[3] |
Caffarelli L A, Nirenberg L, Spruck J. The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian. Acta Mathematca, 1985, 155: 261-301
CrossRef
Google scholar
|
[4] |
Chou K S, Wang X J. A variational theory of the Hessian equation. Communications on Pure and Applied Mathematics, 2001, 54: 1029-1064
CrossRef
Google scholar
|
[5] |
Colesanti A, Salani P. Hessian equations in non-smooth domains. Nonlinear Analysis TMA, 1999, 38: 803-812
CrossRef
Google scholar
|
[6] |
Guan B. The Dirichlet problem for a class of fully nonlinear elliptic equations. Communications in Partial Differential Equations, 1994, 19: 399-416
CrossRef
Google scholar
|
[7] |
Trudinger N S. On the Dirichlet problem for Hessian equations. Acta Mathematica, 1995, 175: 151-164
CrossRef
Google scholar
|
[8] |
Trudinger N S. Weak solutions of Hessian equations, (English summary). Communications in Partial Differential Equations, 1997, 22: 1251-1261
CrossRef
Google scholar
|
[9] |
Trudinger N S, Wang X J. Hessian measures II. Annals of Mathematics, 1999, 150(2): 579-604
CrossRef
Google scholar
|
[10] |
Urbas J I E. On the existence of nonclassical solutions for two class of fully nonlinear elliptic equations. Indiana University Mathematics Journal, 1990, 39: 355-382
CrossRef
Google scholar
|
/
〈 | 〉 |