The Mizohata complex
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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 $\omega$References
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Additional Information
- Abdelhamid Meziani
- Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
- MR Author ID: 239413
- Email: meziani@servax.fiu.edu
- Received by editor(s): August 12, 1994
- Received by editor(s) in revised form: June 27, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 1029-1062
- MSC (1991): Primary 35F05; Secondary 58A10
- DOI: https://doi.org/10.1090/S0002-9947-97-01854-0
- MathSciNet review: 1401780