DARBOUX EQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIANMANIFOLDS WITH NONNEGATIVE CURVATURE IN R^3

The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate on the boundary is contained. As some applications the smooth isometric embeddings of positively and nonnegatively curved disks into Rs are constructed.