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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Mizohata complex

Author: Abdelhamid Meziani
Journal: Trans. Amer. Math. Soc. 349 (1997), 1029-1062
MSC (1991): Primary 35F05; Secondary 58A10
MathSciNet review: 1401780
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Abstract: This paper deals with the local solvability of systems of first order linear partial differential equations defined by a germ $\omega $ at $0\in \mathbb {R}^{n+1}$ of a $\mathbb {C}$-valued, formally integrable ($\omega \wedge d\omega =0$), 1-form with nondegenerate Levi form. More precisely, the size of the obstruction to the solvability, for $(q-1)$-forms $u$, of the equation

\begin{equation*}du\wedge \omega =\eta \wedge \omega ,\end{equation*}

where $\eta $ is a given $q$-form satisfying $d\eta \wedge \omega =0$ is estimated in terms of the De Rham cohomology relative to $\omega $

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Abdelhamid Meziani
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199

Received by editor(s): August 12, 1994
Received by editor(s) in revised form: June 27, 1995
Article copyright: © Copyright 1997 American Mathematical Society