DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC COMPLEX MONGE-AMPERE EQUATION

We consider the Dirichlet problem [GRAPHICS] where Omega is a bounded open set of C-n with regular boundary, g and phi are sufficiently smooth functions, and g is non-negative. We prove that, under additional hypotheses on g and phi, if vertical bar det phi(ij) - g vertical bar C-s* is sufficiently small the problem has a plurisubharmonic solution.