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Double layer potential : ウィキペディア英語版
Double layer potential
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
:u(\mathbf) = \frac \int_S \rho(\mathbf) \frac\frac|} \,d\sigma(\mathbf)
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
:u(\mathbf) = \int_S \rho(\mathbf)\frac P(\mathbf-\mathbf)\,d\sigma(\mathbf)
where ''P''(y) is the Newtonian kernel in ''n'' dimensions.
==See also==

*Potential theory
*Electrostatics
*Laplacian of the indicator

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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