Dirichlet problem for degenerate elliptic complex Monge-Ampere equation

Abstract

We consider the Dirichlet problem det (∂2u/ ∂zi∂zj) = g(z, u) in Ω, u|∂Ω = φ, where Ω is a bounded open set of ℂn with regular boundary, g and φ are sufficiently smooth functions, and g is non-negative. We prove that, under additional hypotheses on g and φ, if | detφij - g|Cs* is sufficiently small the problem has a plurisubharmonic solution.