At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

We consider the classical water wave problem described by the Euler equations with a free
surface under the influence of gravity over a flat bottom. We construct two‐dimensional …

In this paper we present the basic theory of the Monge-Ampere equation together with a
selection of geometric applications, mainly to affine geometry. First we introduce the Monge …

On the second boundary value problem for equations of Monge-Ampere type Page 1 J. reine
angew. Math. 487 (1997), 115—124 Journal fr die reine und angewandte Mathematik © Walter …

In conjunction with applications to optimal transportation and conformal geometry, there has
been considerable research activity in recent years devoted to fully nonlinear, elliptic second …

This paper is concerned with the existence of globally smooth solutions for the second
boundary value problem for certain Monge-Ampere type equations and the application to …

We establish the existence and stability of multidimensional transonic shocks for the Euler
equations for steady potential compressible fluids. The Euler equations, consisting of the …

We prove the existence of a classical solution to a Neumann type problem for nonlinear
elliptic equations of Monge‐Ampère type. The methods depend upon the establishment of a …

In this paper we establish the existence and uniqueness of a transonic shock for the steady
flow through a general two‐dimensional nozzle with variable sections. The flow is governed …