We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone.

The multistochastic Monge–Kantorovich problem on the product X = ? i 1 n of spaces is a generalization multimarginal problem. For given integer number ? k < we consider minimization ? c d ? ? inf space measures with fixed projections onto every × … for arbitrary set indices { , } ? . In this paper study basic properties problem, including well-posedness, existence dual solution, boundedness and...

El objetivo de este artículo se enfoca en el rescate la vida y obra del músico nicolaita Salvador Guerrero Monge (1893-1956). conocimiento su actividad musical México adquiere relevancia actualidad por haber sido alumno, profesor director Academia Bellas Artes Universidad Michoacana San Nicolás Hidalgo sus primeros años existencia. camino para lograr éxito investigación basó análisis documentos...

The Monge-Kantorovich problem is to move one distribution of mass onto another as efficiently as possible, where Monge’s original criterion for efficiency [19] was to minimize the average distance transported. Subsequently studied by many authors, it was not until 1976 that Sudakov showed solutions to be realized in the original sense of Monge, i.e., as mappings from R to R [23]. A second proof...

Local Regularity of the Complex Monge-Ampère Equation Yu Wang In this thesis, we study the local regularity of the complex Monge-Ampère equation, (√ −1∂∂̄u )n = fdx where √ −1∂∂̄u stands for the complex Hessian form and dx the Lebesgue measure. The underline idea of our work is to consider this equation as a full-nonlinear equation and apply modern theory and techniques of elliptic PDEs. Our main...

We consider the obstacle problem for the degenerated Monge-Amp ere equation. We prove the existence of the greatest viscosity sub-solution,and the C 1;1-regularity. Then the solution satisses the concave uniformly elliptic equation. We use the author's previous work to show the C 1;;-regularity of the free boundary. Finally, we discuss the stability of the free boundary. In this paper, we consi...

We prove that c-cyclically monotone transport plans π optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani’s book. We emphasize that we do not need any regularity condi...