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Integral Representations for Second-Order Elliptic Systems in the Plane

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Abstract

A fundamental solution matrix for elliptic systems of the second order with constant leading coefficients is constructed. It is used to obtain an integral representation of functions belonging to the Hölder class in a closed domain with a Lyapunov boundary. In the case of an infinite domain, these functions have power-law asymptotics at infinity. The representation is used to study a mixed-contact boundary value problem for a second-order elliptic system with piecewise constant leading coefficients. The problem is reduced to a system of integral equations that are Fredholm in the domain and singular at its boundary.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, 119333, Moscow, Russia

    A. P. Soldatov

  2. Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia

    A. P. Soldatov

  3. National Research University “Moscow Power Engineering Institute”, 111250, Moscow, Russia

    A. P. Soldatov

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  1. A. P. Soldatov
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Correspondence to A. P. Soldatov.

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Translated by I. Ruzanova

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Soldatov, A.P. Integral Representations for Second-Order Elliptic Systems in the Plane. Comput. Math. and Math. Phys. 64, 118–137 (2024). https://doi.org/10.1134/S0965542524010147

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