Steklov eigenvalues for the Lamé operator in linear elasticity

In this paper we study Steklov eigenvalues for the Lam\'e operator which arise in theory of linear elasticity. eigenproblem spectral parameter appears a Robin boundary condition, linking traction and displacement. To establish existence countable spectrum problem, present an extension Korn's inequality. We also show that proposed conforming Galerkin scheme provides convergent approximations to true eigenvalues. A standard finite element method is used conduct numerical experiments on 2D 3D domains support our theoretical findings.