On Some Problems of Bitsadze–Samarsky Type for the Poisson Equation

The paper is devoted to the study of the solvability of some nonlocal boundary value problems for the Poisson equation in the unit ball. Nonlocal conditions are specified in the form of a connection between the values of the unknown function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. Theorems on the existence and uniqueness of solutions to the studied problems are proved. An explicit form of the Green’s function and an integral representation of solutions to the studied problems are constructed.