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Mayer brackets and solvability of PDEs - II

Author(s): Boris Kruglikov; Valentin Lychagin
Journal: Trans. Amer. Math. Soc. 358 (2006), 1077-1103.
MSC (2000): Primary 35N10, 58A20, 58H10, 35A30
Posted: April 22, 2005
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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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Additional Information:

Boris Kruglikov
Affiliation: Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway
Email: kruglikov@math.uit.no

Valentin Lychagin
Affiliation: Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway
Email: lychagin@math.uit.no

DOI: 10.1090/S0002-9947-05-03724-4
PII: S 0002-9947(05)03724-4
Keywords: Mayer bracket, Spencer cohomology, Weyl tensor, integrals, characteristics, symbols, compatibility of PDEs
Received by editor(s): December 16, 2002
Received by editor(s) in revised form: April 15, 2004
Posted: April 22, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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