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), 3937-3949

MSC (2010):
Primary 35C10; Secondary 35F05

DOI:
https://doi.org/10.1090/S0002-9939-2011-10826-8

Published electronically:
March 11, 2011

MathSciNet review:
2823040

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 one-to-one 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, 13560-970 Brazil

Email:
dattori@icmc.usp.br

**A. Meziani**

Affiliation:
Department of Mathematics, Florida International University, Miami, Florida 33199

Email:
meziani@fiu.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-10826-8

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:
Mei-Chi Shaw

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.