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)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Fejfr, Journal für reine und angewandte Mathematik, Vol. 137 (1909)
Christoffel, Annali di Matematica, 2D Ser. Vol. I (1867)
Schwarz, Journal für reine und angewandte Mathematik, Vol. LXX (1869), p. 105ff.
A. Weinstein, Der Kontinuitätsbeweis des Abbildungssatzes für Polygone, Mathematische Zeitschrift, Vol. XXI (1924), pp. 72—84.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1929 Verlag Von Julius Springer
About this chapter
Cite this chapter
Kellogg, O.D. (1929). The Logarithmic Potential. In: Foundations of Potential Theory. Die Grundlehren der Mathematischen Wissenschaften, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-90850-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-90850-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-88995-0
Online ISBN: 978-3-642-90850-7
eBook Packages: Springer Book Archive