On the influence of the irregularity of the domain boundary on the solution of the boundary value problem for the Laplace equation

An inhomogeneous boundary value problem with mixed boundary conditions for the Laplace equation in a domain representing a perturbation of a rectangle in which one of its sides is replaced by some (irregular) curve is considered. An estimate is obtained for the difference between the generalized solutions of the perturbed and unperturbed problems in the first order Sobolev space on the general domain of their definition.