A symmetry problem

Volume 92 / 2007

A. G. Ramm Annales Polonici Mathematici 92 (2007), 49-54 MSC: 31A25, 35J05, 35J15 DOI: 10.4064/ap92-1-5


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.


  • A. G. RammMathematics Department
    Kansas State University
    Manhattan, KS 66506-2602, U.S.A.

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