This paper is devoted to study a fundamental system of equations in plane Linear Elasticity Theory, the two-dimensional Lamé–Navier system. We rewrite them in a compressed form in terms of the Cauchy–Riemann operators and it allows us to solve a kind of Riemann problem for this system. A generalized Teodorescu operator, to be introduced here, provides the means for obtaining the explicit solution of this problem for a very wide classes of regions, including those with a fractal boundary.

中文翻译：

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分形域上的平面Lamé-Navier系统

本文致力于研究平面线性弹性理论中的基本方程组，即二维Lamé-Navier系统。我们根据考奇-黎曼算子以压缩形式重写它们，这使我们可以解决此系统的黎曼问题。将在此处介绍的广义Teodorescu算子提供了一种方法，可用于针对非常广泛的区域类别（包括具有分形边界的区域）获得该问题的显式解决方案。