University of California, San Diego
La Jolla, California, U. S. A.
The homogeneous Navier equations \[ \nabla^2 {\bf u}+\omega\nabla(\nabla\cdot {\bf u})={\bf 0} ; \omega=\frac{\lambda+\mu}{\mu}=\frac{1}{1-2\nu} \] with homogeneous boundary conditions of place or traction admit non-trivial solutions when $\omega$ takes values in a set of points (lying of course outside the physical range for Poisson's ratio) called the Cosserat Spectrum. The properties of the Spectrum and the corresponding eigenfunctions were studied by S.G. Mikhlin who proved completeness, and orthogonality. Applications to Solid Mechanics and Fluid Mechanics are presented.
Reference:
[1] X. Markenscoff \& M. Paukshto ``On the Cosserat Spectrum Theory and Application'' {\it Proc. Roy. Soc. London} A, 454, 631-43 (1998). }