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On Elliptic Systems of Two Equations on the Plane

  • A. P. Soldatov
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

We considered an elliptic second order system on the plane consisting of two equations with constant (and only leading) coefficients. An explicit representation of the general solution of this system is given via the so-called J-analytic functions. A classification of systems with respect to the Dirichlet problem is given. Explicit expressions for the generalized potentials of a double layer are derived and their applications to solution of the Dirichlet problem are described. The results are illustrated by the example of the Lamé system of plane elasticity theory.

Keywords

Elliptic systems Analytic functions Bitsadze representation Dirichlet problem Generalized potentials of a double layer Lamé system 

Mathematics Subject Classification (2010)

Primary 35J47 35J57 Secondary 31A10 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • A. P. Soldatov
    • 1
  1. 1.Federal Research Center “Computer Science and Control” of Russian Academic of SciencesMoscowRussia

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