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  "body": "\n## Summary\n\nA double layer potential is the potential of a layer of dipoles spread over a surface, with dipoles pointing along the normal.\nIt is the integral of the normal derivative of the [[fundamental solution of the Laplacian|BSJ8X2XRN9]] against a density on the boundary of a domain.\nIt is [[harmonic|0DEB0JMN0W]] off the surface, and its value jumps across the surface by exactly the density, as the [[jump relations|J58YA8QNNX]] say.\nThis jump makes it the standard tool for turning the [[Dirichlet problem|8D56GQ4AG8]] into a Fredholm integral equation, see the [[boundary integral method|QQ62R5ZAXJ]].\n\n## Explanations\n\n### L1 human\n\nPut a thin sheet of tiny magnets on a surface, each with its north pole just outside and its south pole just inside.\nThe potential they create is a double layer potential.\nWhen you cross the sheet, the potential jumps up by the strength of the magnets at that place.\nFor the unit sphere in space with constant strength $1$, the potential is $-1$ inside the sphere and $0$ outside.\n",
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