On potential theory for the generalized bi-axially symmetric elliptic equation in the plane

Fundamental solutions of the generalized biaxially symmetric elliptic equation are expressed in terms of the well-known Appel hypergeometric function in two variables, the properties of which are necessary for studying boundary value problems for the above equation. In this paper, using some properties of the Appel hypergeometric function, we prove limit theorems and derive integral equations for the double- and simple-layer potentials and apply the results of the constructed potential theory to the study of the Dirichlet problem for a two-dimensional elliptic equation with two singular coefficients in a domain bounded in the first quarter of the plane.Fundamental solutions of the generalized biaxially symmetric elliptic equation are expressed in terms of the well-known Appel hypergeometric function in two variables, the properties of which are necessary for studying boundary value problems for the above equation. In this paper, using some properties of the Appel hypergeometric function, we prove limit theorems and derive integral equations for the double- and simple-layer potentials and apply the results of the constructed potential theory to the study of the Dirichlet problem for a two-dimensional elliptic equation with two singular coefficients in a domain bounded in the first quarter of the plane.A