On the boundary integral equation method of solving boundary value problems for the two dimensional Laplace equation

We consider approach based on the integral representation of solutionsin domain which consists of bounded and unbounded parts thatgives us opportunity to reduce different transmission type problems toconnected with them equivalent boundary equations of the first and the second kind.We suppose also that solutions of some of these boundary problems are unbounded at infinity.Interior and exterior Dirichlet and Neumann boundary valueproblems for Laplace equation are restrictions of the solutionsos more general this transmission problems.Interior Neumann and exterior Dirichlet boundary value problems we also can solve usingintegral equation of the second kind that have not unique solution.Corresponding modified equations are constructed in this case and solutions of obtained equations are unique.We also show correctness of all obtained boundary equations of the second typegiven on closed Lipschitz curve in some Hilbert spaceswithout compactness of corresponding integral operators.