On the Dirichlet problem for a class of augmented Hessian equations

In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global second order derivative estimates for the solutions to the Dirichlet problem in bounded domains. The results extend the corresponding results in the previous paper [12] from the Monge–Ampère type equations to the more general Hessian type equations.