For the boundary value problem of diffraction of an external disturbance by a local penetrable body with smooth surface, we construct an integral representation of the solution based on a linear combination of single and double layer potentials with densities distributed over a common auxiliary interior surface. A complete mathematical justification of this representation is given.

中文翻译：

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可穿透体衍射三维问题中场的积分表示

对于具有光滑表面的局部可穿透体对外部扰动的衍射边界值问题，我们基于密度分布在公共辅助内表面上的单层和双层势的线性组合构建解的积分表示。给出了这种表示的完整数学证明。