## A characterization of the sphere in terms of single-layer potentials.(English)Zbl 0752.31003

Summary: Let $$\Omega$$ be a bounded smooth domain in $$\mathbb{R}^ n$$, and suppose the single-layer potential of $$\partial\Omega$$ coincides for $$y\notin\overline\Omega$$ with the function $$c| y|^{-1}$$ $$(c>0)$$. Then $$\partial\Omega$$ is a sphere centered at the origin.

### MSC:

 31B15 Potentials and capacities, extremal length and related notions in higher dimensions
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### References:

 [1] Dov Aharonov, M. M. Schiffer, and Lawrence Zalcman, Potato kugel, Israel J. Math. 40 (1981), no. 3-4, 331 – 339 (1982). · Zbl 0496.31006 [2] O. D. Kellogg, Foundations of potential theory, 4th printing, Ungar, New York, 1970. · Zbl 0152.31301
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