By using the Mellin integral transformation, we obtain the solutions of axisymmetric problems of the theory of elasticity for a cone, namely, of the first and mixed boundary-value problems and the problem of torsion. It is shown that, in the cases where one of the boundary conditions on the entire surface of the cone or on a part of its surface is inhomogeneous and possesses the inversion symmetry and the other boundary condition is homogeneous, some components of the solution also have the inversion symmetry.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 4, pp. 83–94, October–December, 2019.
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Ostryk, V.І. Inversion Symmetry of the Solutions of Axisymmetric Problems of the Theory of Elasticity for a Cone. J Math Sci 265, 438–453 (2022). https://doi.org/10.1007/s10958-022-06063-9
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DOI: https://doi.org/10.1007/s10958-022-06063-9