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

Abstract

In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{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.

Keywords

• exterior dirichlet problem
• complex k-hessian equation
• k-subharmonic function
• gradient estimate
• 35b65
• 35j25