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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Properties of solutions of a class of planar elliptic operators with degeneracies
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by P. L. Dattori da Silva and A. Meziani PDF
Proc. Amer. Math. Soc. 139 (2011), 3937-3949 Request permission

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 $Lw=Aw+B\overline {w}$.
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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
  • MR Author ID: 785140
  • Email: dattori@icmc.usp.br
  • A. Meziani
  • Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
  • MR Author ID: 239413
  • Email: meziani@fiu.edu
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2823040