Boundary Hölder estimates for nonlinear singular elliptic equations

Abstract In this paper we study the Dirichlet problem of a class of nonlinear elliptic equations which includes Monge–Ampere equation, K -Hessian equation and the usual linear elliptic equation. This problem becomes singular near the boundary of the domain. By carefully constructing sub-solutions we obtain the boundary Holder estimate for the convex solution to the problem when the domain satisfies exterior sphere condition.