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Global solvability for a class of overdetermined systems. (English) Zbl 1158.58011
The paper continues the study [J. Funct. Anal. 200, No. 1, 31–64 (2003; Zbl 1034.32024)] of a particular locally integrable structure on $$\mathbb T^3$$ associated with a smooth, real, closed 1-form $$b$$ on $$\mathbb T^2$$. When $$b$$ is exact, then a necessary and sufficient condition of global solvability is connectedness of all the sublevel and superlevel sets of the global primitive of $$b$$. This follows from a general result of F. Cardoso and J. Hounie [Proc. Am. Math. Soc. 65 117–124 (1977; Zbl 0335.58015)].
Now, the authors extend the result to the “incommensurable” case, when $$b$$ is not exact. The modified necessary and sufficient condition refers to the primitive of the pull-back of $$b$$ on the universal covering $$\mathbb R^2 \to \mathbb T^2$$.

##### MSC:
 58J10 Differential complexes 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs
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##### References:
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