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

Author(s): A. Alexandrou Himonas; Gerson Petronilho
Journal: Trans. Amer. Math. Soc. 358 (2006), 4809-4820.
MSC (2000): Primary 35H10, 35B20
Posted: January 24, 2006
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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: 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
Posted: 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.
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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