The Dirichlet problem for Monge-Ampere equations in a hermitian metric

Let X be a C-infinity strongly pseudoconvex hermitian compact manifold with boundary. We solve Dirichlet problems of the form det del(mu)(lambda)phi = F(x, del phi; phi) on X, phi = u on partial derivative X, where F is an element of C-infinity (T X x R) is an everywhere positive function and u is an element of C-infinity (partial derivative X). (C) Elsevier, Paris.