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 previou...

We compare various notions of weak subsolutions to degenerate complex Monge-Ampere flows, showing that they all coincide. This allows us show the viscosity solution coincides with envelope pluripotential subsolutions. Dedicated Duong Hong Phong on occasion his 65th birthday.