The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

Abstract

Abstract In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ⧹ Ω {{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C 1 , 1 {C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.