On the Effect of Irregularity of the Domain Boundary on the Solution of a Boundary Value Problem for the Laplace Equation

We consider an inhomogeneous boundary value problem with mixed boundary conditions for the Laplace equation in a domain representing a perturbation \(\Pi _\gamma \) of a rectangle \(\Pi \) where one of its sides is replaced by some curve \(\gamma \) of minimal smoothness. An estimate is obtained for the difference between the solutions of the perturbed and unperturbed problems in the norm of the Sobolev space \( H^1\) on their common domain.