  A nonlocal contact problem for two-dimensional linear elliptic equations is
stated and investigated. The method of separation of variables is used to find
the solution of a stated problem in case of Poisson's equation. Then the more
general problem with nonlocal multipoint contact conditions for elliptic
equation with variable coefficients is considered and the iterative method to
solve the problem numerically is constructed and investigated. The uniqueness
and existence of the regular solution is proved. The iterative method allows to
reduce the solution of a nonlocal contact problem to the solution of a sequence
of classical boundary value problems.
