scholarly journals A Comparison Principle for Parabolic Complex Monge–Ampère Equations

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Hoang-Son Do ◽  
Thanh Cong Ngoc Pham
Keyword(s):  
Comparison Principle ◽  
Monge Ampere

On a class of generalized Monge–Ampère type equations

2019 ◽  
Vol 22 (05) ◽  
pp. 1950005
Author(s):  
Weifeng Qiu ◽  
Lan Tang
Keyword(s):  
Dirichlet Problem ◽  
Comparison Principle ◽  
Generalized Solutions ◽  
Complete Proof ◽  
Monge Ampere

In this paper, we consider generalized solutions to the Dirichlet problem for a class of generalized Monge–Ampère equations. For such generalized solutions, we give a complete proof for the so-called comparison principle.

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.

Monge–Ampère of Pac-Man

2019 ◽  
Vol 114 (3) ◽  
pp. 343-352
Author(s):  
Norm Levenberg ◽  
Sione Ma’u
Keyword(s):  
Monge Ampere

scholarly journals Monge–Ampère measures on subvarieties

2015 ◽  
Vol 423 (1) ◽  
pp. 94-105 ◽  
Author(s):  
Per Åhag ◽  
Urban Cegrell ◽  
Hoàng Hiệp Phạm
Keyword(s):  
Monge Ampere
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