A symmetry problem
Volume 92 / 2007
Annales Polonici Mathematici 92 (2007), 49-54
MSC: 31A25, 35J05, 35J15
DOI: 10.4064/ap92-1-5
Abstract
Consider the Newtonian potential of a homogeneous bounded body $D\subset \mathbb R^3$ 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.
