• Corpus ID: 246431215

# 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}
}
• Published 31 January 2022
• Mathematics
(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. For complex Monge-Ampère equation, following the theory of Evans-Krylov(see  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  which proves…
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• 1990