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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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