Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application


Author: G. Petronilho
Journal: Trans. Amer. Math. Soc. 363 (2011), 6337-6349
MSC (2010): Primary 35A01, 35F05, 35H10
Published electronically: July 20, 2011
MathSciNet review: 2833557
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The main purpose of this paper is to present a class of real vector fields defined on a torus for which the concepts of global hypoellipticity and global smooth solvability are equivalent. Furthermore, such a vector field is globally hypoelliptic if and only if its adjoint is globally hypoelliptic, and therefore we can reduce it to its normal form. As an application, we study global $ C^\infty$ solvability for certain classes of sub-Laplacians.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 35A01, 35F05, 35H10

Retrieve articles in all journals with MSC (2010): 35A01, 35F05, 35H10


Additional Information

G. Petronilho
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos São Carlos, SP 13565-905, Brazil
Email: gersonpetro@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05359-6
PII: S 0002-9947(2011)05359-6
Keywords: Global hypoellipticity, global solvability, normal form.
Received by editor(s): October 20, 2009
Published electronically: July 20, 2011
Additional Notes: The author was partially supported by CNPq and Fapesp.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.