This research demonstrates new solutions for the Lamé system in an infinite cone, suggesting significant progress in elasticity theory.
The Lamé system of elasticity theory in an infinite circular cone in R³ 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.
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S. I. Bezrodnykh (2025) studied this question.
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