C^2,α-estimate for Monge-Ampere equations with Hölder-continuous right hand side

2014/06/23 by Chen, Xiuxiong, Wang, Yuanqi
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.5825

Abstract

We present a somewhat new proof to the C^2,α-aprori estimate for the uniform elliptic Monge-Ampere equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the C^α^′-norm of the right hand side of the equation, 0

Related

• A \mathcal C^2,α estimate of the complex Monge-Ampère equation
• Pointwise C^2,α estimates at the boundary for the Monge-Ampere equation
• The \mathcal C^2,α estimate of complex Monge-Ampere equation
• Interior Estimates for Monge-Ampère Equation in Terms of Modulus of Continuity
• A Remark On C^2,α-Regularity of the Complex Monge-Ampère Equation