# Balayage

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**Balayage** is a French word meaning scanning or sweeping.

In potential theory, a mathematical discipline, **balayage** is a method devised by Henri Poincaré for reconstructing a harmonic function in a domain from its values on the boundary of the domain.^{[1]}

In modern terms, the **balayage operator** maps a measure *μ* on a closed domain *D* to a measure *ν* on the boundary *∂ D*, so that the Newtonian potentials of *μ* and *ν* coincide outside *D*. The procedure is called balayage since the mass is "swept out" from *D* onto the boundary.

For *x* in *D*, the balayage of *δ*_{x} yields the harmonic measure *ν*_{x} corresponding to *x*. Then the value of a harmonic function *f* at *x* is equal to

## References

- ↑ {{#invoke:citation/CS1|citation |CitationClass=citation }}