$C^{2,\alpha}$-estimate for Monge-Ampere equations with   H\"older-continuous right hand side
  We present a somewhat new proof to the $C^{2,\alpha}$-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 $C^{\alpha^{\prime}}-$norm of the right hand side of the equation, $0<\alpha<\alpha^{\prime}$. 
Xiuxiong Chen, Yuanqi Wang
math.AP math.DG