We complement a previous result concerning a converse of the mean-value property for smooth superharmonic functions. The case of harmonic functions was treated by Kuran and an improvement was given by Armitage and Goldstein.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-1-7, author = {Robert Dalmasso}, title = {On the mean-value property of superharmonic functions}, journal = {Annales Polonici Mathematici}, volume = {93}, year = {2008}, pages = {85-90}, zbl = {1135.31002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-1-7} }
Robert Dalmasso. On the mean-value property of superharmonic functions. Annales Polonici Mathematici, Tome 93 (2008) pp. 85-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-1-7/