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On Elliptic Systems of Two Equations on the Plane

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Analysis as a Life

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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.

Dedicated to Professor Heinrich G. W. Begher on the occasion of his 80th birthday

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of Russian Academic of Sciences, Moscow, Russia

    A. P. Soldatov

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  1. A. P. Soldatov
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Editors and Affiliations

  1. Department of Economics, Belarusian State University, Minsk, Belarus

    Sergei Rogosin

  2. Mathematics Department, Yeditepe University, Ataşehir, Istanbul, Turkey

    Ahmet Okay Çelebi

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Soldatov, A.P. (2019). On Elliptic Systems of Two Equations on the Plane. In: Rogosin, S., Çelebi, A. (eds) Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02650-9_14

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