Boundary regularity for Monge-Ampere equations with unbounded right hand side

We consider Monge-Ampere equations with right hand side f that degenerate to infinity near the boundary of a convex domain Omega, which are of the type dct D(2)u = f in Omega, f similar to d(partial derivative Omega)(-alpha) near partial derivative Omega where d(partial derivative Omega) represents the distance to partial derivative Omega and -alpha is a negative power with alpha is an element of (0, 2). We study the boundary regularity of the solutions and establish a localization theorem for boundary sections.