Let μ be a positive measure with finite support in ℜn (n≧2). Then we show that there is a bounded open set Ω, containing the support of μ, whose single-layer potential coincides with the potential of μ outside Ω.
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Shahgholian, H. Existence of quadrature surfaces for positive measures with finite support. Potential Anal 3, 245–255 (1994). https://doi.org/10.1007/BF01053435
Mathematics Subject Classifications (1991)
- Quadrature surface
- positive Dirac masses
- harmonic functions