Abstract

In previous works ([4–8]), the author studied the general approach to solving mixed boundary, spectral, and initial-boundary transmission problems. In this paper, this approach is applied to the mixed boundary transmission problem of the linear theory of elasticity. On the basis of the corresponding Green formulas the solution of the problem can be represented as the sum of the solutions of auxiliary problems containing a given function only in one place. As a result, four auxiliary problems are obtained. We find their weak solutions using Green’s formulas. And then we conclude that the solution of the original problem is the sum of the auxiliary solutions.

中文翻译：

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线性弹性理论的混合边界传输问题

摘要

在以前的工作中（[4-8]），作者研究了解决混合边界、光谱和初始边界传输问题的一般方法。本文将该方法应用于线性弹性理论的混合边界传输问题。根据相应的格林公式，问题的解可以表示为仅在一个地方包含给定函数的辅助问题的解之和。结果，得到四个辅助问题。我们使用格林公式找到他们的弱解。然后我们得出结论，原问题的解是辅助解的总和。