Global regularity for a class of Monge-Ampère type equations

In this paper we are concerned with the global regularity of solutions to the Dirichlet problem for a class of Monge-Ampère type equations. By employing the concept of (a, η) type domain, we emphasize that the boundary regularity depends on the convexity of the domain in nature. The key idea of our proof is to provide more effective global Hölder estimates of convex solutions to the problem based on carefully choosing auxiliary functions and constructing sub-solutions.