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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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##### References:
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