On modified Bitsadze–Samarskiy problem

We study the non-local boundary value problem which is an analogue of the Bitsadze–Samarskiy problem. For the two-dimensional case we reduce this problem to the local boundary value problem, more exactly to the Dirichlet problem for the analogue of the Laplace equation on the stratified set. Using the Poincare–Perron method we establish that the solution is the upper envelope of the set of subharmonic functions taking given values on the boundary.