A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains

The spectra of the elasticity and piezo-electricity systems for a solid with a sharp peak point on the boundary, which is free of traction, are not discrete. An algebraic criterion of non-empty continuous spectrum is found for the Neumann problem for rather arbitrary formally self-adjoint elliptic systems of second-order differential equations on a sharp peak-shaped domain. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).