Boundary value problems of dirichlet-neumann type for the three-dimensional elliptic equation with two singular coefficients.: Boundary value problems of dirichlet-neumann type for the three-dimensional elliptic equation with two singular coefficients. - Tulakova, Ziyodaxon (MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS, 2024)
Abstract: In the present work, two Dirichlet-Neumann type boundary value problems for a threedimensional elliptic equation with two singular coefficients are investigated. Using an "abc" method, the uniqueness for the solution of the mixed problems is proved. Applying a method of Green‘s functions, we are able to find the solution of the problem in an explicit form, in finding which the properties of the Appel and Gauss hypergeometric functions are essentially used.