The mathcal C^(2,α) estimate of complex Monge-Ampere equation
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alphamathcalcomplexequationestimatemonge-ampmonge-ampereprove
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We prove that any $\mathcal C^{1,1}$ solution to complex Monge-Amp\`ere equation $det(u_{i\bar{j}})=f$ with $0<f\in\mathcal C^{\alpha}$ is in $\mathcal C^{2,\alpha}$ for $\alpha\in (0,1)$.
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