scholarly journals Optimal global asymptotic behavior of the solution to a singular monge-ampère equation

2020 ◽  
Vol 19 (2) ◽  
pp. 1129-1145 ◽  
Author(s):  
Zhijun Zhang ◽  
Keyword(s):  
Asymptotic Behavior ◽  
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.

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 Convex solutions of Monge-Ampère equations and systems: Existence, uniqueness and asymptotic behavior

2020 ◽  
Vol 10 (1) ◽  
pp. 371-399
Author(s):  
Meiqiang Feng
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Type System ◽  
Power Type ◽  
Sharp Estimates ◽  
Convex Solution ◽  
Existence And Nonexistence ◽  
Monge Ampere

Abstract In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates. Then we analyze the existence and nonexistence of nontrivial radial convex solutions to Monge-Ampère systems, which includes some new ingredients in the arguments. Furthermore, the asymptotic behavior of nontrivial radial convex solutions for Monge-Ampère systems is also considered. Finally, as an application, we obtain sufficient conditions for the existence of nontrivial radial convex solutions of the power-type system of Monge-Ampère equations.

scholarly journals Asymptotic behavior at infinity of solutions of Monge-Ampère equations in half spaces

2020 ◽  
Vol 269 (1) ◽  
pp. 326-348 ◽  
Author(s):  
Xiaobiao Jia ◽  
Dongsheng Li ◽  
Zhisu Li
Keyword(s):  
Asymptotic Behavior ◽  
Monge Ampere
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