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  "body": "\n## Summary\n\nA single layer potential is the potential produced by a charge spread over a surface with a given density.\nIt is the integral of the [[fundamental solution of the Laplacian|BSJ8X2XRN9]] against the density times surface measure on the boundary of a domain.\nIt is [[harmonic|0DEB0JMN0W]] off the surface and continuous across it, while its normal derivative jumps by the density, as the [[jump relations|J58YA8QNNX]] say.\nTogether with the [[double layer potential|EG8Z3FWV9A]], it turns boundary value problems for the Laplace equation into integral equations on the boundary.\n\n## Explanations\n\n### L1 human\n\nPaint electric charge onto a thin shell, with more charge in some places and less in others.\nThe electric potential that this painted charge creates in space is a single layer potential.\nAway from the shell it is a smooth harmonic function, and when you cross the shell its value does not jump, but its slope does.\nFor a sphere in space with charge spread evenly, the potential is constant inside the sphere and falls off like $1/\\abs{x}$ outside it.\n",
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