A Remark On C^2,α-Regularity of the Complex Monge-Ampère Equation

2011/11/03 by Wang Yu, Wang, Yu
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1111.0902

openalex publication_date 2011/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the C^2,α-regularity of the solution u of the equation [det(u_k j) = f, f^1/n ∈ C^α, f ≥ λ] under the assumption in upper bound of Δu. Our result settles down the regularity problem related to the paper \citeTian (also see \citeZhang).

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