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The equations determining intermediate integrals for Monge-Ampère PDE
Author(s):
R.
J.
Alonso-Blanco
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2357-2360.
MSC (2000):
Primary 35A30, 58A15
Posted:
March 25, 2004
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Abstract:
In this note we will find the differential equations determining the intermediate integrals for Monge-Ampère equations in an arbitrary number of variables.
References:
-
- 1.
- J. N. Clelland, On the intermediate integral for Monge-Ampère equations, Proc. Amer. Math. Soc. 128 (2000), no. 2, 527-531. MR 2000c:35046
- 2.
- E. Goursat, Leçons sur l'intégration des équations aux dérivées partielles du second ordre, vol. I, Gauthier-Villars, Paris, 1890.
- 3.
- V. V. Lychagin, Local classification of nonlinear first order partial differential equations, Uspekhi Math. Nauk. 30 (Russian); English translation, Russian Math. Surveys 30 (1975), 105-176.
- 4.
- V. V. Lychagin, Contact geometry and second-order nonlinear differential equations, Uspekhi Mat. Nauk 34:1 (1979), 137-165 (Russian); English translation, Russian Math. Surveys 34:1 (1979), 149-180. MR 80h:58057
- 5.
- J. Muñoz-Díaz, Ecuaciones diferenciales I, Universidad de Salamanca, Salamanca, 1982. (Spanish)
- 6.
- L. V. Zil'bergleit, Intermediate integrals of the Monge-Ampère equations. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1999, , no. 9, 16-25; translation in Russian Math. (Iz. VUZ) 43 (1999), no. 9, 13-22 (2000). MR 2001f:58008
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Additional Information:
R.
J.
Alonso-Blanco
Affiliation:
Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, E-37008 Salamanca, Spain
Email:
ricardo@usal.es
DOI:
10.1090/S0002-9939-04-07468-4
PII:
S 0002-9939(04)07468-4
Keywords:
Nonlinear partial differential equation,
Monge-Amp\`{e}re equation,
jet,
intermediate integral,
contact manifold
Received by editor(s):
May 5, 2003
Posted:
March 25, 2004
Additional Notes:
The author was partially funded by Junta de Castilla y León under contract SA077/03
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2004,
American Mathematical Society
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