A Localization Property of Viscosity Solutions to the Monge-Ampere Equation and their Strict Convexity

1990 ◽  
Vol 131 (1) ◽  
pp. 129 ◽  
Author(s):  
L. A. Caffarelli
Keyword(s):  
Viscosity Solutions ◽  
Strict Convexity ◽  
Localization Property ◽  
Monge Ampere

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

scholarly journals Viscosity solutions to quaternionic Monge–Ampère equations

2016 ◽  
Vol 140 ◽  
pp. 69-81 ◽  
Author(s):  
Dongrui Wan ◽  
Wei Wang
Keyword(s):  
Viscosity Solutions ◽  
Monge Ampere

scholarly journals Viscosity solutions of the Monge–Ampère equation with the right hand side in Lp

2007 ◽  
pp. 221-233
Author(s):  
Barbara Brandolini ◽  
Cristina Trombetti ◽  
Anna Lisa Amadori
Keyword(s):  
Viscosity Solutions ◽  
Right Hand ◽  
The Right ◽  
Monge Ampere

scholarly journals Pluripotential solutions versus viscosity solutions to complex Monge–Ampère flows

2021 ◽  
Vol 17 (3) ◽  
pp. 971-990
Author(s):  
Vincent Guedj ◽  
Chinh H. Lu ◽  
Ahmed Zeriahi
Keyword(s):  
Viscosity Solutions ◽  
Monge Ampere

Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

2020 ◽  
Vol 20 (4) ◽  
pp. 769-781
Author(s):  
Limei Dai ◽  
Jiguang Bao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Entire Solutions ◽  
Perron Method ◽  
The Cauchy Problem ◽  
Monge Ampere

AbstractIn this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation-u_{t}\det D^{2}u=f(x,t)and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.

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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