Properties of solutions of a class of planar elliptic operators with degeneracies
Authors:
P. L. Dattori da Silva and A. Meziani
Journal:
Proc. Amer. Math. Soc. 139 (2011), 39373949
MSC (2010):
Primary 35C10; Secondary 35F05
Published electronically:
March 11, 2011
MathSciNet review:
2823040
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Abstract: In this paper we investigate properties of solutions of first and second order elliptic equations that degenerate along a simple closed curve in . These equations are generated by a valued vector field . To the vector field , we associate the second order operator , where is a valued function. We establish a onetoone correspondence between the solutions of the equation and those of an associated first order equation of type .
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Additional Information
P. L. Dattori da Silva
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, São Carlos, SP, 13560970 Brazil
Email:
dattori@icmc.usp.br
A. Meziani
Affiliation:
Department of Mathematics, Florida International University, Miami, Florida 33199
Email:
meziani@fiu.edu
DOI:
http://dx.doi.org/10.1090/S000299392011108268
Keywords:
Elliptic equations,
series representation,
normalization
Received by editor(s):
April 22, 2010
Received by editor(s) in revised form:
September 9, 2010
Published electronically:
March 11, 2011
Additional Notes:
The first author was supported in part by CNPq and FAPESP
Communicated by:
MeiChi Shaw
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
