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Abstract <p> The Lamé system of elasticity theory in an infinite circular cone in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{R}^3\)</EquationSource> </InlineEquation> with the condition of vanishing of displacements at the conical surface is considered. With the help of the Papkovich–Neuber representation for displacements, a new set of solutions of the Lamé system is constructed that identically satisfy a boundary condition on a conical surface and exhibit power-law growth at infinity. </p>

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Application of the Papkovich–Neuber Formula for Finding Solutions of the Lamé System in a Cone

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • S. I. Bezrodnykh

摘要

Abstract

The Lamé system of elasticity theory in an infinite circular cone in \(\mathbb{R}^3\) with the condition of vanishing of displacements at the conical surface is considered. With the help of the Papkovich–Neuber representation for displacements, a new set of solutions of the Lamé system is constructed that identically satisfy a boundary condition on a conical surface and exhibit power-law growth at infinity.