A remark on the continuous subsolution problem for the complex Monge-Ampère equation

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 is also given if the right hand side is locally dominated by capacity.

arXiv comment8 pages

References in corpus (1)

• Hölder continuous solutions to Monge-Ampère equations

Cited by in corpus (2)

• The Hölder continuous subsolution theorem for complex Hessian equations
• The Continuous Subsolution Problem for Complex Hessian Equations