Existence and estimates of solutions to a singular Dirichlet problem for the Monge-Ampere equation

Given a strictly convex, smooth, and bounded domain Omega in R-n we establish the existence of a negative convex solution in C-infinity Omega boolean AND C((Omega) over bar) with zero boundary value to the singular Monge-Ampere equation det(D(2)u) = p(x)g(-u). An associated Dirichlet problem will be employed to provide a necessary and sufficient condition for the solvability of the singular boundary value problem. Estimates of solutions will also be given and regularity of solutions will be deduced from the estimates. (c) 2007 Elsevier Inc. All rights reserved.