Fundamental solutions of a class of degenerate elliptic equation

Abstract

In this paper, for the elliptic equation with two lines of different order of degeneration, given in the first quarter of the plane , four fundamental solutions are constructed that are expressed by Appell's hypergeometric functions of two variables. By means the decomposition formula of the Appell's function in products of the Gauss hypergeometric function, it is proved that the constructed fundamental solutions possess a logarithmic singularity for .