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Potentials play an important role in solving boundary value problems forelliptic equations. In the middle of the last century, a potential theory wasconstructed for a two-dimensional elliptic equation with one singularcoefficient. In the study of potentials, the properties of the fundamentalsolutions of the given equation are essentially and fruitfully used. At thepresent time, fundamental solutions of a multidimensional elliptic equationwith several singular coefficients are already known. In this paper, weinvestigate the double- and simple-layer potentials for this kind of ellipticequations. Results from potential theory allow us to represent the solution ofthe boundary value problems in integral equation form. By using a decompositionformula and other identities for the Lauricella's hypergeometric function inmany variables, we prove limiting theorems and derive integral equationsconcerning a densities of the double- and simple-layer potentials. The obtainedresults are applied to find an explicit solution of the Dirichlet problem forthe generalized singular elliptic equation in the some part of themultidimensional ball.

Double- and simple-layer potentials for generalized singular elliptic equations and their applications to the solving the Dirichlet problem