On Multilayer Films on the Boundary of a Half-Space

Generalized boundary conditions on multilayer films bounding a half-space and consisting of alternating infinitely thin strongly and weakly permeable layers are derived. The solution of the problem for the Laplace equation in a half-plane $D$ bounded by a three-layer film is expressed in simple quadratures in terms of the solution of the classical Dirichlet problem in $D$ without a film.