A priori estimates for the complex Monge-Ampère equation after Krylov

2025/07/29 by Dinew, Sławomir, Sroka, Marcin
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.21729

Abstract

We establish an analytic proof for the Krylov C^1,1 estimates for solutions of degenerate complex Monge-Ampère equation. We also provide an analytic proof of the Bedford-Taylor interior C^1,1 estimate.

Citations

• Determinant majorization and the work of Guo-Phong-Tong and Abja-Olive
• Open problems in pluripotential theory
• Interior regularity of fully nonlinear degenerate elliptic equations, II: real and complex Monge-Ampère equations
• Probability measures related to geodesics in the space of Kähler metrics
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian

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