Isolated Singularities of Harmonic Functions

  • Lavi Karp
  • Harold S. Shapiro
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 145)


The main result of this paper gives a sufficient condition for removability of an isolated singularity of a harmonic function. The condition is given in terms of Newtonian capacity. In addition, an application to an approximation problem is presented.


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  1. 1.
    C. A. Berenstein, R. Gay: Complex Variables, Springer, New York, 1997.Google Scholar
  2. 2.
    W. K. Hayman, L. Karp, H. S. Shapiro: Newtonian capacity and quasi balayage, Rend. Mat. Appl. 20, no. 7 (2000), 93–129.zbMATHMathSciNetGoogle Scholar
  3. 3.
    U. Kuran: n—Dimensional extensions of theorems on conjugate functions, Proc. London Math. Soc. 15, no. 3 (1965), 713–730.CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    N. S. Landkof: Foundation of Modern Potential Theory, Springer, Berlin, 1972.CrossRefGoogle Scholar
  5. 5.
    M. Sakai: Solution to the obstacle problem as a Green potential, J. Analyse Math. 44 (1984/85), 97–116.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2003

Authors and Affiliations

  • Lavi Karp
    • 1
  • Harold S. Shapiro
    • 2
  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael
  2. 2.Department of MathematicsRoyal Institue of TechnologyStockholmSweden

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