A characterization of the sphere in terms of single-layer potentials
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- by Henrik Shahgholian PDF
- Proc. Amer. Math. Soc. 115 (1992), 1167-1168 Request permission
Abstract:
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.References
- Dov Aharonov, M. M. Schiffer, and Lawrence Zalcman, Potato kugel, Israel J. Math. 40 (1981), no. 3-4, 331–339 (1982). MR 654588, DOI 10.1007/BF02761373 O. D. Kellogg, Foundations of potential theory, 4th printing, Ungar, New York, 1970.
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 1167-1168
- MSC: Primary 31B20
- DOI: https://doi.org/10.1090/S0002-9939-1992-1162956-7
- MathSciNet review: 1162956