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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

##### MSC:
 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