Neumann problem for Monge-Ampere type equations revisited.

This paper concerns a priori second order derivative estimates of solutions the Neumann problem for Monge-Amp\`ere type equations in bounded domains n dimensional Euclidean space. We first establish double normal estimate on boundary under an appropriate notion domain convexity. Then, assuming barrier condition linearized operator, we provide complete proof global elliptic solutions, as previously studied our earlier work. also consider extensions to degenerate case, both regular and strictly matrix cases.