The Steklov eigenproblem for a micropolar elastic solid

Abstract

We study the Steklov eigenvalue problem for a linear, isotropic micropolar (Cosserat) elastic solid, where the spectral parameter enters boundary conditions that link tangential tractions to tangential boundary fields. We formulate the problem in strong and weak forms, identify the Dirichlet-to-Neumann map on the boundary, and prove discreteness of the spectrum. Using a microlocal analysis of this map, we establish a Weyl law with an explicit coefficient expressed in terms of the Cosserat moduli. We also analyze spectral stability under high-frequency boundary perturbations.