论文标题
均质复合物$ k $ hessian方程的外部差异问题
The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation
论文作者
论文摘要
在本文中，我们考虑了外部域中的均匀复杂的K-Hessian方程$ \ MATHBB {C}^n \setMinusΩ$。我们通过构造近似解决方案来证明$ c^{1,1} $解决方案的存在和独特性。我们的关键是建立统一的梯度估计和二阶估计。
In this paper, we consider the homogeneous complex k-Hessian equation in an exterior domain $\mathbb{C}^n\setminusΩ$. 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.
