On exceptional sets on the boundary and uniqueness of a solution of the second and third boundary value problems for an elliptic equation

The question is studied of the uniqueness of a solution of the third (in particular, the second) boundary value problem for a linear elliptic equation of second order in the case where the boundary conditions are prescribed everywhere except on some exceptional set of points of the boundary. In terms of Hausdorff measure, restrictions on the exceptional set are obtained under which the space $L_p$ is a uniqueness class for the problem considered.
Bibliography: 9 titles.