Monge-Ampère equations and characteristic connection functors. (English. Russian original) Zbl 1022.58009
Izv. Math. 65, No. 6, 1243-1290 (2001); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 6, 173-222 (2001).
The contact equivalence problem of Monge-Ampère equations is reduced with the help of characteristic functors to the equivalence problem of affine connections. Criteria of contact equivalence for a large class of elliptic and hyperbolic equations are deduced. [See also the author, Izv. Math. 60, No. 2, 425-451 (1996); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 60, No. 2, 195-220 (1996; Zbl 0881.35024) and Sb. Math. 188, No. 5, 771-797 (1997); translation from Mat. Sb. 188, No. 5, 131-157 (1997; Zbl 0895.53021)].
Reviewer: Maido Rahula (Tartu)
MSC:
| 58J05 | Elliptic equations on manifolds, general theory |
| 58J45 | Hyperbolic equations on manifolds |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
