GLOBAL SOLUTIONS AND EXTERIOR DIRICHLET PROBLEM FOR MONGE-AMPERE EQUATION IN R2

Monge-Ampere equation det(D(2)u) = f in two dimensional spaces is different in nature from their counterparts in higher dimensional spaces. In this article we employ new ideas to establish two main results for the Monge-Ampere equation defined either globally in R-2 or outside a convex set. First, we prove the existence of a global solution that satisfies a prescribed asymptotic behavior at infinity, if f is asymptotically close to a positive constant. Then we solve the exterior Dirichlet problem if data are given on the boundary of a convex set and at infinity.