The Logarithmic Potential

  • Oliver Dimon Kellogg
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (volume 31)

Abstract

We have seen in Chapter VI, § 7 (p. 172), that logarithmic potentials are limiting forms of Newtonian potentials. We have seen also that harmonic functions in two dimensions, being special cases of harmonic functions in Space, in that they are independent of one coördinate, partake of the properties of harmonic functions in space. The only essential differences arise from a change in the definition of regu- larity at infinity, and the character of these differences has been amply illustrated in the exercises at the close of Chapter IX (p. 248)

Keywords

Assure Nite WEINSTEIN Veri iLly 

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References

  1. L. Fejfr, Journal für reine und angewandte Mathematik, Vol. 137 (1909)Google Scholar
  2. Christoffel, Annali di Matematica, 2D Ser. Vol. I (1867)Google Scholar
  3. Schwarz, Journal für reine und angewandte Mathematik, Vol. LXX (1869), p. 105ff.Google Scholar
  4. A. Weinstein, Der Kontinuitätsbeweis des Abbildungssatzes für Polygone, Mathematische Zeitschrift, Vol. XXI (1924), pp. 72—84.CrossRefGoogle Scholar

Copyright information

© Verlag Von Julius Springer 1929

Authors and Affiliations

  • Oliver Dimon Kellogg
    • 1
  1. 1.Mathematics in Harvard UniversityCambridgeUSA

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