(untitled) (Journal of Partial Differential Equations, 2009)
In the present paper the regularity of solutions to Dirichlet problem of degenerate elliptic Monge-Ampère equations is studied. Let Ω⊂R^2 be smooth and convex. Suppose that u∈C^2(Ω) is a solution to the following problem: det(u_ij) = K(x) f (x,u,Du) in Ω with u = 0 on ∂Ω. Then u∈C^∞(Ω) provided that f (x,u,p) is smooth and positive in Ω×R×R^2, K > 0 in Ω and near ∂Ω, K=d^mK, where d is the distance to ∂Ω, m some integer bigger than 1 and K smooth and positive on Ω.