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

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.

See also[edit]

• Single layer potential
• Potential theory
• Electrostatics
• Laplacian of the indicator

References[edit]

• Courant, Richard; Hilbert, David (1962), Methods of Mathematical Physics, Volume II, Wiley-Interscience.
• Kellogg, O. D. (1953), Foundations of potential theory, New York: Dover Publications, ISBN 978-0-486-60144-1.
• Shishmarev, I.A. (2001) [1994], "Double-layer potential", Encyclopedia of Mathematics, EMS Press.
• Solomentsev, E.D. (2001) [1994], "Multi-pole potential", Encyclopedia of Mathematics, EMS Press.