Singularities of solutions for Monge-Ampère equations (Q2564834)

The paper is concerned with Monge-Ampère equations of hyperbolic type. First, the characteristic method of Darboux-Goursat in two dimensional space is described. Next, using a representation of equations by differential forms, such a method is extended to higher dimensions provided the equations have a special structure. The second part of the paper is devoted to study singularities of solutions of the Cauchy problem in dimension two, after reduction of the given second order equation to a first order one via ``intermediate integrals''. Some useful examples to illustrate the method are exhibited.