On the range of unsolvable systems induced by complex vector fields

We provide criteria for local unsolvability of first-order differential systems induced by complex vector fields employing techniques from the theory of locally integrable structures. Following Hörmander’s approach to study locally unsolvable equations, we obtain analogous results in the differential complex associated to a locally integrable structure provided that it is not locally exact in three different scenarios: top-degree, Levi-nondegenerate structures and co-rank 1 structures.

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Published in: Partial Differential Equations and Applications
License: https://creativecommons.org/licenses/by/4.0
See article on publisher's website: https://dx.doi.org/10.1007/s42985-023-00260-0