Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Published electronically: March 11, 2011
MathSciNet review: 2823040
Full-text PDF Free Access

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 $\mathbb {R}^2$. These equations are generated by a $\mathbb {C}$-valued vector field $L$. To the vector field $L$, we associate the second order operator $\mathbb {P}=\mathrm {Re}\left [L\overline {L}+p L \right ]$, where $p$ is a $\mathbb {C}$-valued function. We establish a one-to-one correspondence between the solutions of the equation $\mathbb {P}u=0$ and those of an associated first order equation of type $Lw=Aw+B\overline {w}$.

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35C10, 35F05

Retrieve articles in all journals with MSC (2010): 35C10, 35F05

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
MR Author ID: 785140

A. Meziani
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
MR Author ID: 239413

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.