1. See also

2. References

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

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

References

• {{citation|first1=Richard|last1=Courant|authorlink1=Richard Courant|first2=David|last2=Hilbert|authorlink2=David Hilbert|title=Methods of Mathematical Physics, Volume II|publisher=Wiley-Interscience|year=1962}}.
• {{Citation | last1=Kellogg | first1=O. D. | title=Foundations of potential theory | publisher=Dover Publications | location=New York | isbn=978-0-486-60144-1 | year=1953}}.
• {{springer|id=d/d033880|title=Double-layer potential|first=I.A.|last=Shishmarev}}.
• {{springer|id=m/m065210|title=Multi-pole potential|first=E.D.|last=Solomentsev}}.

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