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Local classification of Monge-Ampère differential equations. (English. Russian original) Zbl 0555.35016
Sov. Math., Dokl. 28, 328-332 (1983); translation from Dokl. Akad. Nauk SSSR 272, 34-38 (1983).
A Monge-Ampère equation on the manifold M is defined as \(\sigma^*_ h(\omega)=0\) where \(\omega\) is a given differential form on the jet bundle \(J^ 1M\) and \(\sigma_ h: M\to J^ 1M\) its section corresponding to the unknown function \(h\in C^{\infty}(M)\). Sufficient conditions for the local contact equivalence of a Monge-Ampère equation to an equation with constant coefficients are given. Normal forms of such equations, in case dim M\(=3\), are listed.
Reviewer: S.V.Duzhin

35G20 Nonlinear higher-order PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
58A20 Jets in global analysis
35Q99 Partial differential equations of mathematical physics and other areas of application
58J99 Partial differential equations on manifolds; differential operators