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 | References | Similar Articles | Additional Information

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 .

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Additional Information

**Paulo A. S. Caetano**

Affiliation:
Department of Mathematics, Universidade Federal de São Carlos, São Carlos, SP, Brazil

Email:
caetano@dm.ufscar.br

**Paulo D. Cordaro**

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

Email:
cordaro@ime.usp.br

DOI:
http://dx.doi.org/10.1090/S0002-9947-2010-04893-7

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.