×

zbMATH — the first resource for mathematics

Global solvability for certain classes of underdetermined systems of vector fields. (English) Zbl 0863.58062
A necessary and sufficient condition is proved for the validity of the global Poincaré lemma, in top degree, in the differential complex attached to certain classes of involutive structures defined over compact manifolds.

MSC:
58J10 Differential complexes
35N10 Overdetermined systems of PDEs with variable coefficients
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Bergamasco, A.P., Cordaro, P.D., Malagutti, P.A.: Globally hypoelliptic systems of vector fields. J. Funct. Anal.114, n 0 2, 267–285 (1993) · Zbl 0777.58041 · doi:10.1006/jfan.1993.1068
[2] Cardoso, F., Hounie, J.: Global solvability of an abstract complex. Proc. Amer. Math. Soc.65, n 0 1, 117–124 (1977) · Zbl 0335.58015 · doi:10.1090/S0002-9939-1977-0463721-8
[3] Cordaro, P.D., Hounie, J.: On local solvability of underdetermined systems of vector fields. Amer. J. Math.112, 243–270 (1990) · Zbl 0708.58025 · doi:10.2307/2374715
[4] Hörmander, L.: Linear partial differential operators. Springer-Verlag, New York 1963 · Zbl 0108.09301
[5] Hörmander, L.: The analysis of linear partial differential operators IV. Springer-Verlag, New York 1985 · Zbl 0612.35001
[6] Hounie, J.: Globally hypoelliptic and globally solvable first order evolution equations. Trans. Amer. Math. Soc.252, 233–248 (1979) · Zbl 0424.35030
[7] Treves, F.: Topological vector spaces, distributions and kernels. Academic Press, New York 1967
[8] Treves, F.: Study of a model in the theory of complexes of pseudodifferential operators. Ann. of Math.104, 269–324 (1976) · Zbl 0354.35067 · doi:10.2307/1971048
[9] Treves, F.: Hypo-analytic structures (local theory). Princeton University Press, Princeton, NJ, 1992 · Zbl 0787.35003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.