A priori estimates for solutions of nonlinear second-order elliptic equations

We consider classes of elliptic equations of the form (x,u,uD²u)=0 for the solutions of which one establishes local and global a priori estimates for D²u=. In particular, one investigates the Monge-Ampere equation, and for its convex solutions one constructs a local and a global estimate for D²u and a local estimate for.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 31–59, 1976.