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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On $C^\infty$ and Gevrey regularity of sublaplacians
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by A. Alexandrou Himonas and Gerson Petronilho PDF
Trans. Amer. Math. Soc. 358 (2006), 4809-4820 Request permission

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
  • MR Author ID: 86060
  • Email: himonas.1@nd.edu
  • Gerson Petronilho
  • Affiliation: Department of Mathematics, Federal University of São Carlos, São Carlos, SP 13565-905, Brazil
  • MR Author ID: 250320
  • Email: gerson@dm.ufscar.br
  • 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.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 4809-4820
  • MSC (2000): Primary 35H10, 35B20
  • DOI: https://doi.org/10.1090/S0002-9947-06-03819-0
  • MathSciNet review: 2231873