Steklov eigenvalues for the Lamé operator in linear elasticity

Abstract

In this paper we introduce the notion of Steklov eigenvalues for the Lamé operator in the theory of linear elasticity. In this eigenproblem the spectral parameter appears on a Robin boundary condition, linking the traction and the displacement. We investigate the spectrum of this problem and study the existence of eigenpairs on Lipschitz domains as well as show that any conforming Galerkin method is able to provide good approximations to this problem. A standard conforming finite element method is used to obtain numerical experiments on 2D and 3D domains to support our theoretical findings.