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Transactions of the American Mathematical Society

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Gevrey solvability and Gevrey regularity in differential complexes associated to locally integrable structures

Authors: Paulo A. S. Caetano and Paulo D. Cordaro
Journal: Trans. Amer. Math. Soc. 363 (2011), 185-201
MSC (2000): Primary 35A07; Secondary 35D10, 35N10
Published electronically: August 24, 2010
MathSciNet review: 2719678
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Abstract: In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, Gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition. As a consequence we obtain the proof of the Gevrey solvability for a first order linear PDE with real-analytic coefficients satisfying the Nirenberg-Treves condition $ ({\mathcal{P}})$.

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Additional Information

Paulo A. S. Caetano
Affiliation: Department of Mathematics, Universidade Federal de São Carlos, São Carlos, SP, Brazil

Paulo D. Cordaro
Affiliation: Department of Mathematics, Universidade de São Paulo, São Paulo, SP, Brazil

Keywords: Local solvability, Gevrey classes, locally integrable structures, hypo-analytic structures
Received by editor(s): November 19, 2007
Received by editor(s) in revised form: July 26, 2008
Published electronically: August 24, 2010
Additional Notes: This research was partially supported by CNPq and Fapesp.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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