scholarly journals Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations I: the d-Concavity and the Comparison Principle

2017 ◽  
Vol 44 (2) ◽  
pp. 469-491 ◽  
Author(s):  
Ha Tien Ngoan ◽  
Thai Thi Kim Chung
Keyword(s):  
Comparison Principle ◽  
Elliptic Solutions ◽  
Monge Ampere

Gradient estimates for Neumann boundary value problem of Monge–Ampère type equations

2016 ◽  
Vol 19 (04) ◽  
pp. 1650041 ◽  
Author(s):  
Feida Jiang ◽  
Ni Xiang ◽  
Jinju Xu
Keyword(s):  
Matrix Function ◽  
Symmetric Matrix ◽  
Type Equation ◽  
Neumann Boundary ◽  
Gradient Estimates ◽  
Neumann Boundary Value Problem ◽  
The Matrix ◽  
Elliptic Solutions ◽  
Monge Ampere ◽  
Gradient Bound

This paper concerns the gradient estimates for Neumann problem of a certain Monge–Ampère type equation with a lower order symmetric matrix function in the determinant. Under a one-sided quadratic structure condition on the matrix function, we present two alternative full discussions of the global gradient bound for the elliptic solutions.

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.

Sign in / Sign up

Export Citation Format

Share Document