# Gradient estimate for complex Monge-Ampere equation with continuous right hand side

@inproceedings{Chen2022GradientEF, title={Gradient estimate for complex Monge-Ampere equation with continuous right hand side}, author={Xiuxiong Chen and Jingrui Cheng}, year={2022} }

(1) The deep work of Kolodziej which states that if e ∈ L(M) for some p > 1, then φ ∈ C for some α ∈ (0, 1). (2) C2,α estimate when the right hand side F ∈ C. For real Monge Ampère equation, this goes back to Caffarelli[2]. For complex Monge-Ampère equation, following the theory of Evans-Krylov(see [15] for details on extension to complex setting), we know [φ]C2,α′ (M,g) is uniformly bounded, for each α ′ < α, if ∆φ is uniformly bounded. (3) The important theorem of Chen-He [5] which proves…

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