Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740002
Author(s):  
Sławomir Kołodziej
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Stability Of Solutions ◽  
Hermitian Manifolds ◽  
Priori Estimates ◽  
Existence And Stability ◽  
Monge Ampere

In this paper, we describe how pluripotential methods can be applied to study weak solutions of the complex Monge–Ampère equation on compact Hermitian manifolds. We indicate the differences between Kähler and non-Kähler setting. The results include a priori estimates, existence and stability of solutions.

scholarly journals On the Neumann Problem for Monge-Ampére Type Equations

2016 ◽  
Vol 68 (6) ◽  
pp. 1334-1361 ◽  
Author(s):  
Feida Jiang ◽  
Neil S. Trudinger ◽  
Ni Xiang
Keyword(s):  
Global Regularity ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Neumann Boundary ◽  
Natural Conditions ◽  
Priori Estimates ◽  
The Neumann Problem ◽  
Monge Ampere ◽  
Oblique Boundary

AbstractIn this paper, we study the global regularity for regular Monge-Ampère type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Ampère case by Lions, Trudinger, and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger, and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.

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