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.References
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Additional Information
- Boris Kruglikov
- Affiliation: Institute of Mathematics and Statistics, University of Tromsø, Tromsø90-37, Norway
- Email: kruglikov@math.uit.no
- Valentin Lychagin
- Affiliation: Institute of Mathematics and Statistics, University of Tromsø, Tromsø90-37, Norway
- Email: lychagin@math.uit.no
- Received by editor(s): December 16, 2002
- Received by editor(s) in revised form: April 15, 2004
- Published electronically: April 22, 2005
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 1077-1103
- MSC (2000): Primary 35N10, 58A20, 58H10, 35A30
- DOI: https://doi.org/10.1090/S0002-9947-05-03724-4
- MathSciNet review: 2187646