  We prove the existence of C^{\infty} local solutions to a class of mixed type
Monge-Ampere equations in the plane. More precisely, the equation changes type
to finite order across two smooth curves intersecting transversely at a point.
Existence of C^{\infty} global solutions to a corresponding class of linear
mixed type equations is also established. These results are motivated by, and
may be applied to the problem of prescribed Gaussian curvature for graphs, the
isometric embedding problem for 2-dimensional Riemannian manifolds into
Euclidean 3-space, and also transonic fluid flow.
