This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lamé operators of elasticity $-{\mathrm{\Delta }}^{⁎}+V$ in terms of suitable norms of the potential V. In particular, this allows to get sufficient conditions on the size of the potential such that the point spectrum of the perturbed operator remains empty. In three dimensions we show full spectral stability under suitable form-subordinated perturbations: we prove that the spectrum is purely continuous and coincides with the non negative semi-axis as in the free case.

中文翻译：

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具有复势的Lamé算子的特征值界和谱稳定性

本文致力于提供非自伴随弹性弹性算子的离散和嵌入特征值位置的定量界限$-{\mathrm{\Delta }}^{⁎}+伏$就电位V的合适范数而言。特别是，这允许获得关于势能大小的充分条件，使得扰动算子的点谱保持为空。在三个维度中，我们在合适的形式从属扰动下显示出完整的光谱稳定性：我们证明光谱是纯连续的，并且与自由情况下的非负半轴重合。