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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On $ C^\infty$ and Gevrey regularity of sublaplacians


Authors: A. Alexandrou Himonas and Gerson Petronilho
Journal: Trans. Amer. Math. Soc. 358 (2006), 4809-4820
MSC (2000): Primary 35H10, 35B20
Published electronically: January 24, 2006
MathSciNet review: 2231873
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Abstract: In this paper we consider zero order perturbations of a class of sublaplacians on the two-dimensional torus and give sufficient conditions for global $ C^\infty$ regularity to persist. In the case of analytic coefficients, we prove Gevrey regularity for a general class of sublaplacians when the finite type condition holds.


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Additional Information

A. Alexandrou Himonas
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: himonas.1@nd.edu

Gerson Petronilho
Affiliation: Department of Mathematics, Federal University of São Carlos, São Carlos, SP 13565-905, Brazil
Email: gerson@dm.ufscar.br

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03819-0
PII: S 0002-9947(06)03819-0
Keywords: Gevrey hypoellipticity, microlocal analysis, perturbations
Received by editor(s): July 29, 2003
Received by editor(s) in revised form: August 5, 2004
Published electronically: January 24, 2006
Additional Notes: The first author was partially supported by the NSF under grant number DMS-9970857, and the second author was partially supported by CNPq.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.