Dirichlet problems for general Monge-Ampère equations (Q1188023)

The present paper is concerned with boundary value problems for a class of general Monge-Ampère equations \(\text{det}(\nabla^ 2 z)=K(x)f(x,z,\nabla z)\) in \(Q\) with constant Dirichlet data on \(\partial\Omega\) where \(f\) is a positive function and \(K\) non-negative and \(\nabla^ 2 z\) denotes the Hessian of \(z\) with respect to a given metric \(ds^ 2\). A result about existence of solutions in \(C^ \infty(\Omega)\) and some applications to differential geometry are given.