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

 

Semilinear hypoelliptic differential operators with multiple characteristics


Author: Nguyen Minh Tri
Journal: Trans. Amer. Math. Soc. 360 (2008), 3875-3907
MSC (2000): Primary 35H10; Secondary 35A08, 35B45, 35B65.
Published electronically: February 13, 2008
MathSciNet review: 2386250
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Abstract:

In this paper we consider the regularity of solutions of semilinear differential equations principal parts of which consist of linear polynomial operators constructed from real vector fields. Based on the study of fine properties of the principal linear parts we then obtain the regularity of solutions of the nonlinear equations. Some results obtained in this article are also new in the frame of linear theory.


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Additional Information

Nguyen Minh Tri
Affiliation: Institute of Mathematics, 18 Hoang Quoc Viet Road, Cau Giay District, 10307 Hanoi, Vietnam
Address at time of publication: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: triminh@math.ac.vn

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04443-7
PII: S 0002-9947(08)04443-7
Keywords: Semilinear differential equations, a priori estimates, maximal hypoellipticity, polynomial operators constructed from real vector fields.
Received by editor(s): August 15, 2006
Published electronically: February 13, 2008
Article copyright: © Copyright 2008 American Mathematical Society