A Viscosity Approach to the Dirichlet Problem for Complex Monge-Ampère Equations

Abstract

The Dirichlet problem for complex Monge-Ampére equations with continuous data is considered. In particular, a notion of viscosity solutions is introduced; a comparison principle and a solvability theorem are proved; the equivalence between viscosity and pluripotential solutions is established; and an ABP-type of $L^{\infty }$-estimate is achieved.

This version contains a new proof of existence of solution, in which semi-continuous functions are avoided. It also gives an estimate of modulus of continuity of solution in terms of datum and subsolution. An corollary of ABP estimate is added. A few changes on presentation have been included

References in corpus (1)

• Singular Kahler-Einstein metrics