Symmetry problems 2
Tom 96 / 2009
Annales Polonici Mathematici 96 (2009), 61-64 MSC: 35J05, 31B20. DOI: 10.4064/ap96-1-5
Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to $c/|x|$ for all sufficiently large $|x|$, where $c>0$ is a constant, then the surface is a sphere.