Аннотация:
In this article we investigate the Neumann problem for a degenerate elliptic equation
in four variables. A fundamental solution is used to construct a solution to the problem. The
fundamental solutions are written by using the Lauricella's hypergeometric functions. The energyintegral method is used to prove the uniqueness of the solution to the problem under consideration.
In the course of proving the existence of the problem solution, differentiation formulas, decomposition
formulas, some adjacent relations formulas and the autotransformation formula of hypergeometric
functions are used. The Gauss–Ostrogradsky formula is used to express problem's solution in an
explicit form.
Ключевые слова и фразы:Neumann problem, energy-integral method, degenerate four-dimensional elliptic equation, Gauss–Ostrogradsky formula, fundamental solutions, Lauricella hypergeometric functions.