Previously, the incompressible limit of the equations of Hookean elastodynamics has been established in the whole space. The present paper is devoted to the study of the incompressible limit in a bounded domain. Here, the main difficulty lies in the interactions between the large operator and the boundary. By designing some delicate semi-norms and energy estimates, we obtain the uniform estimates of the solutions. As a result, the incompressible limit is established by classical compactness argument.

中文翻译：

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有限域内Hookean弹性动力学的不可压缩极限

以前，已经在整个空间中建立了Hookean弹性动力学方程的不可压缩极限。本文致力于有界域中不可压缩极限的研究。在此，主要困难在于大型操作员与边界之间的相互作用。通过设计一些精细的半范数和能量估计，我们获得了解决方案的统一估计。结果，不可压缩极限是通过经典的紧凑性论证建立的。