On the range of unsolvable systems induced by complex vector fields

A. V. da Silva

doi:10.1007/s42985-023-00260-0

On the range of unsolvable systems induced by complex vector fields

A. V. da Silva^*

^*Corresponding author for this work

Texas A&M University at Qatar

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	41
Journal	Partial Differential Equations and Applications
Volume	4
Issue number	5
DOIs	https://doi.org/10.1007/s42985-023-00260-0
Publication status	Published - Oct 2023
Externally published	Yes

Keywords

First-order systems of PDEs
Locally integrable structures
Locally unsolvable systems

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10.1007/s42985-023-00260-0

Cite this

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title = "On the range of unsolvable systems induced by complex vector fields",

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 H{\"o}rmander{\textquoteright}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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doi = "10.1007/s42985-023-00260-0",

language = "English",

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N2 - 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.

AB - 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.

KW - First-order systems of PDEs

KW - Locally integrable structures

KW - Locally unsolvable systems

UR - https://www.scopus.com/pages/publications/85169684285

U2 - 10.1007/s42985-023-00260-0

DO - 10.1007/s42985-023-00260-0

M3 - Article

AN - SCOPUS:85169684285

SN - 2662-2963

VL - 4

JO - Partial Differential Equations and Applications

JF - Partial Differential Equations and Applications

IS - 5

M1 - 41

ER -

On the range of unsolvable systems induced by complex vector fields

Abstract

Keywords

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