scholarly journals A Liouville theorem for solutions of the Monge–Ampère equation with periodic data

2004 ◽  
Vol 21 (1) ◽  
pp. 97-120 ◽  
Author(s):  
L Caffarelli ◽  
YanYan Li
Keyword(s):  
Liouville Theorem ◽  
Periodic Data ◽  
Monge Ampere

scholarly journals A Liouville theorem of parabolic Monge-AmpÈre equations in half-space

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Ziwei Zhou ◽  
◽  
Jiguang Bao ◽  
Bo Wang ◽  
Keyword(s):  
Half Space ◽  
Liouville Theorem ◽  
Monge Ampere

scholarly journals A Mean Value Formula and a Liouville Theorem for the Complex Monge–Ampère Equation

2018 ◽  
Vol 2020 (3) ◽  
pp. 853-867
Author(s):  
Chao Li ◽  
Jiayu Li ◽  
Xi Zhang
Keyword(s):  
Liouville Theorem ◽  
Hermitian Matrix ◽  
Type Theorem ◽  
Mean Value ◽  
Complete Riemannian Manifold ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Nonnegative Ricci Curvature ◽  
Monge Ampere ◽  
Mean Value Formula

Abstract In this paper, we prove a mean value formula for bounded subharmonic Hermitian matrix valued function on a complete Riemannian manifold with nonnegative Ricci curvature. As its application, we obtain a Liouville type theorem for the complex Monge–Ampère equation on product manifolds.

THE LIOUVILLE THEOREM INVOLVING QUANTUM EFFECT

1986 ◽  
Vol 6 (2) ◽  
pp. 201-211 ◽  
Author(s):  
Keda Bao ◽  
Fusui Liu
Keyword(s):  
Liouville Theorem ◽  
Quantum Effect

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.

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