In this paper we introduce the notion of Steklov eigenvalues for the Lamé operator in the theory of linear elasticity. In this eigenproblem the spectral parameter appears on a Robin boundary condition, linking the traction and the displacement. We investigate the spectrum of this problem and study the existence of eigenpairs on Lipschitz domains as well as show that any conforming Galerkin method is able to provide good approximations to this problem. A standard conforming finite element method is used to obtain numerical experiments on 2D and 3D domains to support our theoretical findings.

中文翻译：

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线性弹性中Lamé算子的Steklov特征值

在本文中，我们介绍了线性弹性理论中Lamé算子的Steklov特征值的概念。在这个本征问题中，谱参数出现在罗宾边界条件上，将牵引力和位移联系在一起。我们调查此问题的范围并研究Lipschitz域上特征对的存在，并证明任何符合标准的Galerkin方法都可以为该问题提供良好的近似。使用标准的符合性有限元方法来获得2D和3D域的数值实验，以支持我们的理论发现。