Single layer potential

Summary

A single layer potential is the potential produced by a charge spread over a surface with a given density. It is the integral of the fundamental solution of the Laplacian against the density times surface measure on the boundary of a domain. It is harmonic off the surface and continuous across it, while its normal derivative jumps by the density, as the jump relations say. Together with the double layer potential, it turns boundary value problems for the Laplace equation into integral equations on the boundary.