Consider the Newtonian potential of a homogeneous bounded body D ⊂ ℝ³ with known constant density and connected complement. If this potential equals c/|x| in a neighborhood of infinity, where c>0 is a constant, then the body is a ball. This known result is now proved by a different simple method. The method can be applied to other problems.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-5,
author = {A. G. Ramm},
title = {A symmetry problem},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {49-54},
zbl = {1209.31004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-5}
}
A. G. Ramm. A symmetry problem. Annales Polonici Mathematici, Tome 92 (2007) pp. 49-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-5/