In potential theory, an area of mathematics, a double layer potential is a solution of Laplace's equation corresponding to the electrostatic or magnetic potential associated to a dipole distribution on a closed surface S in three-dimensions.
Thus a double layer potential u(x) is a scalar-valued function of x ∈ R3 given by
4 π
ρ (
∂ ν
d σ (
where ρ denotes the dipole distribution, ∂/∂ν denotes the directional derivative in the direction of the outward unit normal in the y variable, and dσ is the surface measure on S. More generally, a double layer potential is associated to a hypersurface S in n-dimensional Euclidean space by means of
where P(y) is the Newtonian kernel in n dimensions.