Double- and simple-layer potentials for a three-dimensional elliptic equation with a singular coefficient and their applications

The double- and simple-layer potentials play an important role in solving boundary value problems for elliptic equations, and in studying this potentials, the properties of the fundamental solutions of the given equation are used. At present, fundamental solutions of the multidimensional Helmholtz equation are known but nevertheless, only for the two-dimensional equations the potential theory was constructed. In this paper we study both potentials for the three-dimensional singular elliptic equation and apply the obtained results to the solving a Dirichlet problem.