Abstract We consider the solution to a transmission problem at a thin layer interface of thickness e > 0 in a mechanical structure. We build a multi-scale expansion for that solution as e → 0 , which enables to replace the thin layer with an improved boundary condition and leads to optimal estimates for the remainders. This short note presents new results when a Dirichlet condition is imposed on the internal boundary of the thin layer and is the counterpart of F. Caubet, D. Kateb, F. Le Louer, J. Elast. 136 (1) (2019) 17–53, where the Neumann case was considered.

中文翻译：

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机械结构中的薄层近似：狄利克雷边界条件情况

摘要 我们考虑了机械结构中厚度 e > 0 的薄层界面传输问题的解决方案。我们为该解决方案构建了一个多尺度扩展 e → 0 ，这使得能够用改进的边界条件替换薄层并导致对剩余部分的最佳估计。当 Dirichlet 条件强加在薄层的内部边界上时，这个简短的注释呈现了新的结果，并且是 F. Caubet、D. Kateb、F. Le Louer、J. Elast 的对应物。136 (1) (2019) 17-53，其中考虑了诺依曼案例。