Two methods of integrating Monge-Ampère’s equations

Abstract

Modifying Monge’s method and Laplace’s one respectively, we shall give two methods of integration of Monge-Ampère’s equations. Although they seem quite different, the equivalence of our two methods will be shown. The first method will be from a point of view different from that of Lewy. The second will present a solution to a problem of Goursat.