Acta Mathematica Vietnamica
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ON THE CAUCHY PROBLEM FOR MULTIDIMENSIONAL MONGE-AMPÈRE EQUATIONS
HA TIEN NGOAN, NGUYEN THI NGApp. 281-298
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.