The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation

Abstract

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

arXiv admin note: text overlap with arXiv:2207.13504

References in corpus (1)

• Second Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian Manifolds