Remarks on global Hölder regularity for a class of Monge-Ampère type equations

Abstract

In this paper, we revisit the global Hölder regularity of nonzero convex solutions to the Dirichlet problem for a class of Monge-Ampère type equations. Based on the comparison principle, by choosing delicate auxiliary functions to construct the subsolutions, we extend the boundary regularity obtained in [Li-Li, Sci. China Math. 65 (3) (2022)] to more general equations, in which the parameters α,β,γ in the boundness condition are less restrictive. Also, the non-decreasing condition there can be replaced with a homogeneous type condition.