On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains

2011 ◽  
Vol 6 (2) ◽  
pp. 221-230 ◽  
Author(s):  
Limei Dai ◽  
Jiguang Bao
Keyword(s):  
Viscosity Solutions ◽  
Exterior Domains ◽  
Hessian Equations ◽  
Uniqueness And Existence

scholarly journals The Dirichlet Problem of Hessian Equation in Exterior Domains

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 666
Author(s):  
Hongfei Li ◽  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Dirichlet Problem ◽  
Viscosity Solutions ◽  
Exterior Domains ◽  
Hessian Equation ◽  
Hessian Equations ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations det D 2 u = f ( x ) .

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