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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 used. At the present time,fundamental solutions of a multidimensional elliptic equation with onedegeneration line are already known. In this paper, we investigate thepotentials of the double- and simple-layers for this equation, with the help ofwhich limit theorems are proved and integral equations containing in the kernelthe density of the above potentials are derived.

Potentials for a multidimensional elliptic equation with one line of degeneration and their applications to boundary value problems