scholarly journals Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge–Ampère Equation in Dimensions Two and Higher

2011 ◽  
Vol 49 (4) ◽  
pp. 1692-1714 ◽  
Author(s):  
Brittany D. Froese ◽  
Adam M. Oberman
Keyword(s):  
Finite Difference ◽  
Viscosity Solutions ◽  
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
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