  Potentials play an important role in solving boundary value problems for
elliptic equations. In the middle of the last century, a potential theory was
constructed for a two-dimensional elliptic equation with one singular
coefficient. In the study of potentials, the properties of the fundamental
solutions of the given equation are essentially and fruitfully used. At the
present time, fundamental solutions of a multidimensional elliptic equation
with several singular coefficients are already known. In this paper, we
investigate the double- and simple-layer potentials for this kind of elliptic
equations. Results from potential theory allow us to represent the solution of
the boundary value problems in integral equation form. By using a decomposition
formula and other identities for the Lauricella's hypergeometric function in
many variables, we prove limiting theorems and derive integral equations
concerning a densities of the double- and simple-layer potentials. The obtained
results are applied to find an explicit solution of the Dirichlet problem for
the generalized singular elliptic equation in the some part of the
multidimensional ball.
