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Mixed Contact Problem for the Lamé System with Piecewise Constant Main Coefficients

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We construct the fundamental matrix of solutions to the Lamé system with constant main coefficients in the general anisotropic case. Using the fundamental matrix, we obtain an integral representation of functions of a Hölder class in a closed domain with Lyapunov boundary. In the case of an infinite domain, the representation is described within the framework of weighted Hölder spaces (of functions with power behavior at infinity). Based on this representation, we can reduce the mixed contact boundary value problem for the Lamé system with piecewise constant main coefficients to a system of integral equations that are Fredholm in the domain and are singular on the boundary. As a result, we establish a Fredholm criterion and indicate the index for this problem.

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Authors and Affiliations

  1. Dalat University, Da Lat, Lam Dong, Viet Nam

    Tran Quang Vuong

  2. Federal Research Center “Computer Science and Control” RAS, 40, Vavilova St., Moscow, 119333, Russia

    A. P. Soldatov

  3. Moscow Center for Fundamental and Applied Mathematics, National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya St., Moscow, 111250, Russia

    A. P. Soldatov

Authors
  1. Tran Quang Vuong
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  2. A. P. Soldatov
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Correspondence to A. P. Soldatov.

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Translated from Problemy Matematicheskogo Analiza 125, 2023, pp. 153-171.

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Vuong, T.Q., Soldatov, A.P. Mixed Contact Problem for the Lamé System with Piecewise Constant Main Coefficients. J Math Sci 276, 168–190 (2023). https://doi.org/10.1007/s10958-023-06732-3

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