Potential Analysis

, Volume 3, Issue 2, pp 245–255 | Cite as

Existence of quadrature surfaces for positive measures with finite support

  • Henrik Shahgholian


Let μ be a positive measure with finite support in ℜ n (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.

Mathematics Subject Classifications (1991)

31B20 35J05 

Key words

Quadrature surface positive Dirac masses harmonic functions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alt, H. W. and Caffarelli, L. A.: ‘Existence and Regularity for a Minimum Problem with Free Boundary’,J. Reine Angew. Math. 325 (1981), 434–448.Google Scholar
  2. 2.
    Shahgholian, H.: ‘Quadrature Surfaces as Free Boundaries’, preprint.Google Scholar
  3. 3.
    Federer, H.:Geometric Measure Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1969).Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Henrik Shahgholian
    • 1
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholm 70Sweden

Personalised recommendations