Global analytic and Gevrey hypoellipticity of sublaplacians under Diophantine conditions
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Abstract:
In this paper we consider the problem of global Gevrey and analytic regularity for a class of partial differential operators on a torus in the form of a sum of squares of vector fields, which may not satisfy the bracket condition. We show that these operators are globally Gevrey or analytic hypoelliptic on the torus if and only if the coefficients satisfy certain Diophantine approximation properties.References
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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
- Received by editor(s): November 15, 1999
- Published electronically: December 4, 2000
- Additional Notes: The author was supported in part by NSF Grant DMS-9970857.
- Communicated by: David S. Tartakoff
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2061-2067
- MSC (1991): Primary 35H05
- DOI: https://doi.org/10.1090/S0002-9939-00-05996-7
- MathSciNet review: 1825918