On the solution of boundary value problems for the laplace equation on the plane with a three-layer film inclusion

We derive analytic formulas that, on the basis of given harmonic functions, permit one to construct solutions of boundary value problems on a plane containing an infinitely thin three-layer film by simple quadratures with the preservation of singular points of the harmonic functions. The three-layer film consists of alternating strongly and weakly permeable layers and has the form of a ray, a segment, or a circle arc.