Английская Википедия:Balayage
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Шаблон:About In potential theory, a mathematical discipline, balayage (from French: balayage "scanning, sweeping") is a method devised by Henri Poincaré for reconstructing an 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 <math>\bar D</math>. The procedure is called balayage since the mass is "swept out" from D onto the boundary.
For x in D, the balayage of δx yields the harmonic measure νx corresponding to x. Then the value of a harmonic function f at x is equal to
- <math> f(x) = \int_{\partial D} f(y) \, d\nu_x(y).</math>
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