Nonlocal Problem for a Three-dimensional Elliptic Equation with Singular Coefficients in a Rectangular Parallelepiped

Abstract

The nonlocal problem for an elliptic equation with two singular coefficients in a rectangular parallelepiped is studied. The uniqueness of the solution of the problem is proved with the use of the method of energy integrals. The spectral Fourier method based on the separation of variables is used to prove the existence of solutions. The solution of the problem is constructed as double Fourier series in terms of a sum of trigonometric and Bessel functions. Under some conditions on parameters and given functions the uniform convergence of the constructed series and its derivatives up to the second order inclusive is proved

Исследована нелокальная задача для эллиптического уравнения с двумя сингулярными коэффициентами в прямоугольном параллелепипеде. Доказательство единственности решения и его построение проведены спектральным методом с использованием разложения в ряд Фурье и Фурье-Бесселя. При некоторых условиях относительно параметров и заданных функций доказана равномерная сходимость построенного ряда