The \mathcal C^2,α estimate of complex Monge-Ampere equation

2010/06/22 by Slawomir Dinew, Sławomir Dinew, Dinew, Slawomir +4
Mathematics · Physics and Astronomy · #32W20 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.CV #msc:32W20

paper · pdf · doi:10.48550/arxiv.1006.4261

8 pages

arxiv created 2010/06/22 · openalex publication_date 2010/06/22 · arxiv updated 2010/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that any \mathcal C^1,1 solution to complex Monge-Ampère equation det(u_ij)=f with 0<f∈\mathcal C^α is in \mathcal C^2,α for α∈ (0,1).

Related

• A \mathcal C^2,α estimate of the complex Monge-Ampère equation
• A Remark On C^2,α-Regularity of the Complex Monge-Ampère Equation
• A priori estimates for the complex Monge-Ampère equation after Krylov
• C^2,α-estimate for Monge-Ampere equations with Hölder-continuous right hand side
• An application of a C²-estimate for a complex Monge-Ampère equation