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

$${\displaystyle u(\mathbf {x} )={\frac {-1}{4\pi ))\int _{S}\rho (\mathbf {y} ){\frac {\partial }{\partial \nu )){\frac {1}{|\mathbf {x} -\mathbf {y} |))\,d\sigma (\mathbf {y} )}$$

More generally, a double layer potential is associated to a hypersurface S in n-dimensional Euclidean space by means of

$${\displaystyle u(\mathbf {x} )=\int _{S}\rho (\mathbf {y} ){\frac {\partial }{\partial \nu ))P(\mathbf {x} -\mathbf {y} )\,d\sigma (\mathbf {y} )}$$