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Neumann resonances in linear elasticity for an arbitrary body. (English) Zbl 0851.35032
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 \(N> 0\).

MSC:
35J15 Second-order elliptic equations
74B05 Classical linear elasticity
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