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Globally hypoelliptic systems of vector fields. (English) Zbl 0777.58041
The authors study the global hypoellipticity of differential operators associated to certain locally integrable structures defined over compact manifolds. They extend results of S. J. Greenfield and N. R. Wallach [Proc. Am. Math. Soc. 31, 112-114 (1972; Zbl 0229.35023)] on global hypoellipticity of vector fields defined on the two dimensional torus. Further connections to locally hypoelliptic overdetermined systems are discussed [see H. M. Maire, Commun. Partial Differ. Equations 5, 331-380 (1980; Zbl 0436.35024)].
Reviewer: N.Jacob (Erlangen)

MSC:
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
65H10 Numerical computation of solutions to systems of equations
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