Bakharev, F. L.; Nazarov, S. A. On the structure of the spectrum for the elasticity problem in a body with a supersharp spike. (Russian, English) Zbl 1224.35395 Sib. Mat. Zh. 50, No. 4, 746-756 (2009); translation in Sib. Math. J. 50, No. 4, 587-595 (2009). Summary: 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. Cited in 9 Documents MSC: 35Q74 PDEs in connection with mechanics of deformable solids 35P05 General topics in linear spectral theory for PDEs 74B05 Classical linear elasticity Keywords:system of elasticity equations; spike; cusp; peak; continuous spectrum PDF BibTeX XML Cite \textit{F. L. Bakharev} and \textit{S. A. Nazarov}, Sib. Mat. Zh. 50, No. 4, 746--756 (2009; Zbl 1224.35395); translation in Sib. Math. J. 50, No. 4, 587--595 (2009) Full Text: EMIS EuDML