International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 57340, 3 pages
doi:10.1155/IJMMS/2006/57340
On the mean value property of superharmonic and
subharmonic functions
Laboratoire LMC-IMAG, Equipe EDP, Tour IRMA, BP 53, Grenoble Cedex 9 38041, France
Received 19 October 2005; Revised 25 January 2006; Accepted 16 February 2006
Copyright © 2006 Robert Dalmasso. 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.
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.