Bitsadze-Samarsky type problems with double involution

Abstract

Abstract In this paper, the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. 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. Using Green’s functions of the classical Dirichlet and Neumann boundary value problems, Green’s functions of the studied problems are constructed and integral representations of solutions to these problems are obtained.

Keywords

• Nonlocal problem
• Poisson equation
• Orthogonal matrix
• Involution
• Dirichlet problem
• Neumann problem