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

 

A similarity principle for complex vector fields and applications


Authors: S. Berhanu, J. Hounie and P. Santiago
Journal: Trans. Amer. Math. Soc. 353 (2001), 1661-1675
MSC (1991): Primary 35F05, 35N10, 35A05; Secondary 35F20, 32F40
Published electronically: November 29, 2000
MathSciNet review: 1806725
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Abstract:

This paper establishes a similarity principle for a class of non-elliptic, smooth complex vector fields in the plane. This principle is used to prove a uniqueness result for a nonlinear Cauchy problem.


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Additional Information

S. Berhanu
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-6094
Email: berhanu@euclid.math.temple.edu

J. Hounie
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, CEP 13.565-905, São Carlos, SP, Brasil
Email: hounie@dm.ufscar.br

P. Santiago
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-6094
Address at time of publication: Departamento de Matemática, Universidade Federal de Pernambuco, CEP 50.740-540, Recife, PE, Brasil
Email: santiago@dmat.ufpe.br

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02673-8
PII: S 0002-9947(00)02673-8
Keywords: Similarity principle, locally solvable vector field
Received by editor(s): October 14, 1998
Received by editor(s) in revised form: October 25, 1999
Published electronically: November 29, 2000
Additional Notes: The first author thanks IMPA of Brazil for an invitation to a pde workshop in July, 1997, that facilitated this work
The second author was partially supported by CNPq, FAPESP and FINEP
The third author was supported partially supported by CNPq
Article copyright: © Copyright 2000 American Mathematical Society