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On the intermediate integral for Monge-Ampere equations

Jeanne Nielsen Clelland
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Abstract

Goursat showed that in the presence of an intermediate integral, the problem of solving a second-order Monge-Ampere equation can be reduced to solving a first-order equation, in the sense that the generic solution of the first-order equation will also be a solution of the original equation. An attempt by Hermann to give a rigorous proof of this fact contains an error; we show that there exists an essentially unique counterexample to Hermann's assertion and state and prove a correct theorem.

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Jeanne Nielsen Clelland. 1998-04-06. On the intermediate integral for Monge-Ampere equations. https://arxiv.org/abs/math/9804029

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