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

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

2011-11-03

arxiv.org/abs/1111.0902v1

Mathematics

Complex Variables

Scientific paper

We prove the $C^{2,\alpha}$-regularity of the solution $u$ of the equation
[\det(u_{\bar{k} j}) = f, \quad f^{1/n} \in C^{\alpha}, \quad f \geq \lambda]
under the assumption in upper bound of $\Delta u$. Our result settles down the
regularity problem related to the paper \cite{Tian} (also see \cite{Zhang}).

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