Smoothness of radial solutions to Monge-Ampère equations Journal Articles

We prove that generalized convex radial solutions to the generalized Monge-Ampère equation det D 2 u = f ( | x | 2 / 2 , u , | ∇ u | 2 / 2 ) \det D^2u = f(|x|^2/2,u,|\nabla u|^2/2) with f f smooth are always smooth away from the origin. Moreover, we characterize the global smoothness of these solutions in terms of the order of vanishing of f f at the origin.