Monge-Ampère equations on the nonstrict convex domains

Quaternionic 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].

Sobolev Regularity for Monge-Ampère Type Equations

In this note we prove that, if the cost function satisfies some necessary structural conditions and the densities are bounded away from zero and infinity, then strictly c-convex potentials arising in optimal transportation belong to W 2,1+κ loc for some κ > 0. This generalizes some recents results [10, 11, 24] concerning the regularity of strictly convex Alexandrov solutions of the Monge-Ampère...

Triple nontrivial radial convex solutions of systems of Monge-Ampère equations

Positive convex solutions of boundary value problems arising from Monge-Ampère equations

In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Ampère equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.

A multigrid scheme for 3D Monge-Ampère equations

The elliptic Monge-Ampère equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community [Tad12, FGN13]. Fast three dimensional solvers are needed, for example in medical image registration, [HZTA04, HRT10, HPM+09, HM07], but are not yet available. We build fast solvers for smooth solutions in three dimensions...