Absence of positive eigenvalues for the linearized elasticity system (Q1882435)

The author considers the linearized isotropic elasticity system defined in an unbounded domain \(\Omega\subset\mathbb{R}^n\) with Lamé coefficients and mass density varying in an unbounded part of \(\Omega\). Two geometric situations are analysed: the whole space \(\mathbb{R}^n\), and a local perturbation of the half-space. In the second situation stress-free boundary conditions are taken. The absence of positive eigenvalues for the considered elasticity operators is proven. In the first step, it is proven that the eigenfunctions vanish on a part of \(\Omega\), and then, in the second step, the unique continuation property of the considered equation is established.