On the range of unsolvable systems induced by complex vector fields

A. V. da Silva ()
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A. V. da Silva: Texas A &M University at Qatar

Partial Differential Equations and Applications, 2023, vol. 4, issue 5, 1-29

Abstract: Abstract 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.

Keywords: Locally unsolvable systems; Locally integrable structures; First-order systems of PDEs; 35A01—Existence problems for PDEs: global existence local existence non-existence; 35F05—Linear first-order PDEs; 58J10—Differential complexes elliptic complexes (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00260-0

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