Neumann resonances in linear elasticity for an arbitrary body
The resonances associated to the Lamé operator \(L\) in the exterior of an arbitrary obstacle in \(\mathbb{R}^3\) with Neumann boundary conditions are analyzed. The resonances are defined as the poles of the meromorphic continuation of the cut-off resolvent from the lower half plane \((\text{Im } y< 0)\) to the whole complex plane \(\mathbb{C}\). The main result of the paper is the following: There exist two infinite sequences \(\{\lambda_j\}\), \(\{\overline \lambda_j\}\) of distinct resonances of the Lamé operator \(L\), such that \(0< \text{Im } \lambda_j\leq C_N|\lambda_j|^{- N}\) for any \(N> 0\).
meromorphic continuation of the cut-off resolvent
scientific article; zbMATH DE number 906555