On the structure of the spectrum for the elasticity problem in a body with a supersharp spike

We establish that the continuous spectrum of the Neumann problem for the system of elasticity equations occupies the entire closed positive real semiaxis in the case that a three-dimensional body with a sharp-spiked cusp whose cross-section contracts to a point with the velocity $O(r^{1+\gamma})$, where $r$ is the distance to the vertex of the spike and $\gamma>1$ is the sharpness exponent.