The double- and simple-layer potentials play an important role in solving boundary value problems for elliptic equations. The desired solution represents a potential of a certain layer with unknown density. One finds it with the help of the theory of Fredholm integral equations of the second kind. The potential, in turn, is expressed via the fundamental solution to the given elliptic equation. At present, fundamental solutions to Helmholtz multidimensional singular equations are known, nevertheless, the potential theory is constructed only for two-dimensional degenerate equations. In this paper, we study the mentioned potentials for a three-dimensional elliptic equation with one singular coefficient and apply the obtained results to solving the Dirichlet problem.

双层势和简单势在解决椭圆方程的边值问题中起着重要作用。所需的解表示具有未知密度的特定层的电势。人们借助第二类Fredholm积分方程的理论找到了它。电位又通过给定椭圆方程的基本解表示。目前，已知亥姆霍兹多维奇异方程的基本解，但是，仅针对二维简并方程构造了势能理论。在本文中，我们研究了具有一个奇异系数的三维椭圆方程的上述势能，并将所得结果用于求解Dirichlet问题。