Abstract
We prove a converse of the mean value property for superharmonic and subharmonic functions. The case of harmonic functions was treated by Epstein and Schiffer.
Open Access
On the mean value property of superharmonic and subharmonic functions
Received19 Oct 2005
Revised25 Jan 2006
Accepted16 Feb 2006
Published14 May 2006
References
B. Epstein and M. Schiffer, “On the mean-value property of harmonic functions,” Journal d'Analyse Mathématique, vol. 14, pp. 109–111, 1965.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol. 224 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNetÜ. Kuran, “On the mean-value property of harmonic functions,” The Bulletin of the London Mathematical Society, vol. 4, pp. 311–312, 1972.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.