Sharp boundary regularity for some degenerate-singular Monge-Ampère equations on k-convex domain

We introduce the concept of k-strictly convexity to describe the accurate convexity of convex domains some directions of which boundary may be flat. Basing this accurate convexity we construct sub-solutions for the Dirichlet problem of some degenerate-singular Monge-Ampere type equations and prove the sharp boundary estimates for convex viscosity solutions of the problem. As a result, we obtain the optimal global Holder regularity of the convex viscosity solutions. (c) 2023 Elsevier Inc. All rights reserved.