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

preprint2010arXivOpen access

We prove that any $\mathcal C^{1,1}$ solution to complex Monge-Ampère equation $det(u_{i\bar{j}})=f$ with $0<f\in\mathcal C^α$ is in $\mathcal C^{2,α}$ for $α\in (0,1)$ .

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

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The C2,α\mathcal C^{2,α}C2,α estimate of complex Monge-Ampere equation

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