On a generalization of the third boundary value problem for the Laplace equation

In this paper we consider the solvability of new classes of boundary value problems for the Laplace equation. The problems under investigation are a generalization of the classical third boundary value problem for the Laplace equation. Theorems on the existence and uniqueness of the solution of the problem are proved. Conditions for the solvability of the problem are found and integral representations of the solution are established.