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Behavior of a Class of Second-order Planar Elliptic Equations with Degeneracies

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Recent Progress in Operator Theory and Its Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 220))

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Abstract

Normalization results are obtained for classes of second-order elliptic equations in \(\mathbb{R}\)which degenerate along a simple closed curve or with an isolated singularity. The behavior of the solutions of the corresponding homogeneous equation in a neighborhood of the degeneracy as well as the maximum principle is studied.

Mathematics Subject Classification (2000). Primary 35J70; Secondary 35A05, 35B50.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida International University, Miami, FL, 33199, USA

    Abdelhamid Meziani

Authors
  1. Abdelhamid Meziani
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Correspondence to Abdelhamid Meziani .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  2. Dept. Mathematics, University of Iowa, MacLean Hall 14, Iowa City, 52242-1419, Iowa, USA

    Raúl E. Curto

  3. , CINVESTAV, IPN - Instituto Politécnico Nacional, Av. IPN 2508, Mexico, D.F., 07360, Distrito Federal, Mexico

    Sergei M. Grudsky

  4. Dept. Mathematics, University of California, San Diego, Gilman Dr. 9500, La Jolla, 92093-0112, California, USA

    J. William Helton

  5. , Departamento di Matemática, Centro de Investigación en Matemáticas, Guanajuato, Gto., 36000, Guanajuato, Mexico

    Raúl Quiroga-Barranco

  6. Departamento de Matemática, CINVESTAV-IPN, Apdo. Postal, México, 07300, Distrito Federal, Mexico

    Nikolai L. Vasilevski

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Meziani, A. (2012). Behavior of a Class of Second-order Planar Elliptic Equations with Degeneracies. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_14

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