Application of the Papkovich–Neuber formula for finding solutions of the Lamé system in a cone

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.