In this paper, we consider the Neumann–Poincaré type operator associated with the Lamé system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two different points determined by Lamé parameters. We show that eigenvalues converge at a polynomial rate on smooth boundaries and the convergence rate is determined by smoothness of the boundary. We also show that they converge at an exponential rate if the boundary of the domain is real analytic.

中文翻译：

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二维弹性Neumann-Poincaré算子特征值的收敛速度

在本文中，我们考虑与线性弹性Lamé系统相关的Neumann–Poincaré型算子。已知如果平面域的边界足够平滑，则其特征值会聚到由Lamé参数确定的两个不同点。我们证明了特征值在平滑边界上以多项式速率收敛，收敛速度由边界的平滑度决定。我们还表明，如果域的边界是真实解析的，则它们以指数速率收敛。