ON THE CAUCHY PROBLEM FOR MULTIDIMENSIONAL MONGE-AMPÈRE EQUATIONS

Ha Tien Ngoan and Nguyen Thi Nga

Abstract

          The Cauchy problem for Monge-Ampère equations with several variables is formulated and reduced to that for a normal system of first-order nonlinear partial differential equations. The noncharacteristic condition for the Cauchy problem of multidimensional Monge-Ampère is given. The local solvability of the noncharacteristic Cauchy problem for these equations in the class of analytic functions is proved.