Inverse boundary value problem for second order elliptic equation with additional integral condition

An inverse boundary value problem for the second order elliptic equation with an additional integral condition of the first kind is investigated. We introduce the definition of a classical solution for the considered inverse boundary value problem reduced to solving of the system of integral equations by the use of the Fourier method. First, the existence and uniqueness of solutions of the system of integral equations are proved by using the method of contraction mappings; and then the existence and uniqueness of classical solutions of the original problem are proved.