The degenerate scale issue for 2D-boundary integral equations and boundary element methods has been already investigated for Laplace equation, antiplane and plane elasticity, bending plate for Dirichlet boundary condition. Recently, the problems of Robin and mixed boundary conditions and of piecewise heterogeneous domains have been considered for the case of Laplace equation. We investigate similar questions for plane elasticity for more general boundary conditions. For interior problems, it is shown that the degenerate scales do not depend on the boundary condition. For exterior problems, the two degenerate scales (homogeneous medium) or two of them (heterogeneous medium) are tightly linked with the behavior at infinity of the solutions. The dependence of this behavior on the boundary conditions is investigated. We give sufficient conditions for the uniqueness of the solution. Numerical applications are provided and validate the set of theoretical results.

中文翻译：

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一般边界条件下分段均匀介质中平面弹性问题的退化尺度

二维边界积分方程和边界元方法的退化尺度问题已经针对拉普拉斯方程、反平面和平面弹性、狄利克雷边界条件的弯曲板进行了研究。最近，已经在拉普拉斯方程的情况下考虑了罗宾和混合边界条件以及分段异质域的问题。我们针对更一般的边界条件研究平面弹性的类似问题。对于内部问题，表明退化尺度不依赖于边界条件。对于外部问题，两个退化尺度（均质介质）或其中两个（非均质介质）与解的无穷大行为紧密相关。研究了这种行为对边界条件的依赖性。我们给出解的唯一性的充分条件。提供了数值应用并验证了理论结果集。