Inpotential theory, an area ofmathematics, adouble layer potential is a solution ofLaplace's equation corresponding to theelectrostatic ormagnetic potential associated to adipole distribution on a closed surfaceS in three-dimensions. Thus a double layer potentialu(x) is a scalar-valued function ofx ∈R³ given by$${\displaystyle u(\mathbf{x})=\frac{-1}{4\pi }{\int }_S\rho (\mathbf{y})\frac{\mathrm{\partial }}{\mathrm{\partial }\nu }\frac{1}{|\mathbf{x}-\mathbf{y}|}d\sigma (\mathbf{y})}$$whereρ denotes the dipole distribution,∂/∂ν denotes the directional derivative in the direction of the outward unit normal in they variable, and dσ is the surface measure onS.

More generally, a double layer potential is associated to ahypersurfaceS inn-dimensionalEuclidean space by means of$${\displaystyle u(\mathbf{x})={\int }_S\rho (\mathbf{y})\frac{\mathrm{\partial }}{\mathrm{\partial }\nu }P(\mathbf{x}-\mathbf{y})d\sigma (\mathbf{y})}$$whereP(y) is theNewtonian kernel inn dimensions.

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

• 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{{citation}}:ISBN / Date incompatibility (help).
• 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.

• Potential theory

• CS1 errors: ISBN date