article

Title: The $\mathcal C^{2,\alpha}$ estimate of complex Monge-Ampere equation

Authors: Slawomir Dinew, Xi Zhang and XiangWen Zhang

Issue: Volume 60 (2011), Issue 5, 1713-1722

Abstract:

$We prove that any $\mathcal{C}^{1,1}$ solution to the complex Monge-Amp\'ere equation $\det(u_{i\bar{\jmath}}) = f$ with $0 < f \in \mathcal{C}^{\alpha}$ is in $\mathcal{C}^{2,\alpha}$ for $\alpha \in (0,1)$.$