The ${\mathcal{C}}^{2,\alpha }$ estimate of complex Monge-Ampere equation

Abstract

We prove that any ${\mathcal{C}}^{1,1}$ solution to complex Monge-Ampère equation $det(u_{i\bar{j}})=f$ with $0<f\in {\mathcal{C}}^{\alpha }$ is in ${\mathcal{C}}^{2,\alpha }$ for $\alpha \in (0,1)$.

8 pages

Cited by in corpus (1)

• Regularity estimates of solutions to complex Monge-Ampère equations on Hermitian manifolds