In this paper, an inverse problem of Tikhonov-Lavrentev kind for the two-dimensional Laplace operator with local boundary conditions is considered. In the early sections, by using of the fundamental solution, a number of necessary conditions in the form of integro-partial differential equations are provided that singularities contained in them are regularized. Then by applying of these necessary conditions and boundary conditions, the unknown functions in the boundary conditions and main problem are presented as a system of integro-partial differential equation.
