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The Galerkin tensor operator, reduction to tetraharmonic equations, and their fundamental solutions

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Abstract

The mathematical apparatus of the Galerkin representation for solving problems of isotropic elasticity theory is generalized to systems originated by linear symmetric tensorial (second-rank) differential fourth-order operators over the symmetric tensor field. These systems are reduced to tetraharmonic equations, and fundamental solutions of these equations in a multidimensional space are given.

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    D. V. Georgievskii

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  1. D. V. Georgievskii
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Correspondence to D. V. Georgievskii.

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Original Russian Text © D.V. Georgievskii, 2015, published in Doklady Akademii Nauk, 2015, Vol. 463, No. 4, pp. 418–421.

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Georgievskii, D.V. The Galerkin tensor operator, reduction to tetraharmonic equations, and their fundamental solutions. Dokl. Phys. 60, 364–367 (2015). https://doi.org/10.1134/S1028335815080030

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  • DOI: https://doi.org/10.1134/S1028335815080030

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