On a Lower Bound of the Cosserat Spectrum for the Second Boundary Value Problem of Elastostatics

Abstract

The boundary value problem with given stresses on the boundary for the Navier (Lamé) equation is under consideration. The Cosserat eigenvalues are those values of a spectral parameter related to the Poisson ratio σ which admit non-trivial solution to the homogeneous boundary value problem. It is known that all finite-multiple Cosserat eigenvalues belong to the ray (-∞, 1/3]. The aim of the paper is to prove that for any convex domain the Cosserat eigenvalues are contained in the interval(-1,1/3]

Keywords:

• Lamé equation
• Cosserat eigenvalues