Boundary C2,αC2,α estimates for Monge–Ampère type equations

In this paper, we obtain global second derivative estimates for solutions of the Dirichlet problem of certain Monge–Ampère type equations under some structural conditions, while the inhomogeneous term is only assumed to be Hölder continuous and bounded away from zero and infinity. These estimates correspond to those for the standard Monge–Ampère equation obtained by Trudinger and Wang (2008) [28] and by Savin (2013) [24], and have natural applications in optimal transportation and prescribed Jacobian equations.