Monotone and consistent discretization of the Monge-Ampère operator
نویسندگان
چکیده
منابع مشابه
Discretization of functionals involving the Monge-Ampère operator
Gradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The numerical applications of this formulation have been limited by the difficulty to compute the Wasserstein distance in dimension > 2. One step of the JKO scheme is equivalent to a variational problem on the space of con...
متن کاملConvergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation
We prove a rate of convergence for smooth solutions of the MongeAmpère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. No rate of convergence was known for the discretization we consider.
متن کاملQuaternionic Monge-ampère Equations
The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in H. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].
متن کاملContinuity Estimates for the Monge-Ampère Equation
In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semi-geostrophic equation arising in meteorology.
متن کاملComplex Monge-ampère of a Maximum
Pluri-subharmonic (psh) functions play a primary role in pluri-potential theory. They are closely related to the operator dd c = 2i∂ ¯ ∂ (with notation d = ∂ + ¯ ∂ and d c = i(¯ ∂ − ∂)), which serves as a generalization of the Laplacian from C to C dim for dim > 1. If u is smooth of class C 2 , then for 1 ≤ n ≤ dim, the coefficients of the exterior power (dd c u) n are given by the n×n sub-dete...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2016
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3080