A Remark on the Continuous Subsolution Problem for the Complex Monge-Ampère Equation

Abstract

Abstract We prove that if the modulus of continuity of a plurisubharmonic subsolution satisfies a Dini-type condition then the Dirichlet problem for the complex Monge-Ampère equation has the continuous solution. The modulus of continuity of the solution also given if the right hand side is locally dominated by capacity.