Potentials for Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem

In earlier research, the double- and simple layer potentials have been successfully applied in solving boundary value problems for two-dimensional elliptic equations. Despite the fact that all fundamental solutions of a three-dimensional elliptic equation with one, two and three singular coefficients were known, the potential theory was not constructed in any case of a singularity. Here, in this paper, our goal is to construct a potential theory corresponding to the three-dimensional elliptic equation with one singular coefficient. We used some properties of Gaussian hypergeometric function to prove the limiting theorems, while deriving integral equations concerning the denseness of potentials.

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