Green's function for the harmonic potential of the three-dimensional wedge transmission problem

摘要

The point-source static potential in a wedge geometry consisting of two homogeneous media is solved via the Kontorovich-Lebedev and Fourier transforms. Inverse transforms enable the solution of Laplace's equation to be expressed in terms of image contributions plus residue sums (Fourier series) of toroidal functions. As in previous wave equation solutions for isovelocity wedges, explicit expressions for the poles that are the site of the residues are exploited when the wedge angle is a rational multiple of π.