Solution of boundary value problems for Laplace's equation in a piecewise homogeneous plane with a parabolic crack (screen)

Boundary value problems for Laplace's equation are considered in a piecewise homogeneous plane divided into two zones by a strongly permeable crack or a weakly permeable screen in the form of a parabola. The desired potentials have prescribed singular points (sources, sinks, etc.). Formulas are derived expressing the potentials in terms of harmonic functions that have the given singular points and describe similar processes in a homogeneous plane.