On the intermediate integral for Monge-Ampere equations

被引：2

作者：

Clelland, JN ^{[1
]}

机构：

[1] Univ Colorado, Dept Math, Boulder, CO 80309 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 02期

关键词：

method of the intermediate integral; Monge-Ampere equations; exterior differential systems;

D O I：

10.1090/S0002-9939-99-05136-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：527 / 531

页数：5