Double layer potential

Summary

A double layer potential is the potential of a layer of dipoles spread over a surface, with dipoles pointing along the normal. It is the integral of the normal derivative of the fundamental solution of the Laplacian against a density on the boundary of a domain. It is harmonic off the surface, and its value jumps across the surface by exactly the density, as the jump relations say. This jump makes it the standard tool for turning the Dirichlet problem into a Fredholm integral equation, see the boundary integral method.