On the intermediate integral for Monge-Ampère equations
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- by Jeanne Nielsen Clelland PDF
- Proc. Amer. Math. Soc. 128 (2000), 527-531 Request permission
Abstract:
Goursat showed that in the presence of an intermediate integral, the problem of solving a second-order Monge-Ampère 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.References
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Additional Information
- Jeanne Nielsen Clelland
- Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309
- Email: Jeanne.Clelland@Colorado.edu
- Received by editor(s): April 6, 1998
- Published electronically: July 8, 1999
- Additional Notes: This research was supported in part by NSF grant DMS-9627403.
- Communicated by: Lesley M. Sibner
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 527-531
- MSC (1991): Primary 35A30; Secondary 58A15
- DOI: https://doi.org/10.1090/S0002-9939-99-05136-9
- MathSciNet review: 1641669