Mayer brackets and solvability of PDEs – II

Kruglikov, Boris; Lychagin, Valentin

doi:10.1090/S0002-9947-05-03724-4

Mayer brackets and solvability of PDEs – II
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by Boris Kruglikov and Valentin Lychagin PDF

Trans. Amer. Math. Soc. 358 (2006), 1077-1103 Request permission

Abstract:

For the Spencer $\delta$-cohomologies of a symbolic system we construct a spectral sequence associated with a subspace. We calculate the sequence for the systems of Cohen-Macaulay type and obtain a reduction theorem, which facilitates computation of $\delta$-cohomologies by reducing dimension of the system. Using this algebraic result we prove an efficient compatibility criterion for a system of two scalar non-linear PDEs on a manifold of any dimension in terms of (generalized) Mayer brackets.

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