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A characterization of the sphere in terms of single-layer potentials


Author: Henrik Shahgholian
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
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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\vert y{\vert^{ - 1}}(c > 0)$. Then $ \partial \Omega $ is a sphere centered at the origin.


References [Enhancements On Off] (What's this?)

  • [ASZ] D. Aharonov, M. M. Schiffer, and L. Zalcman, Potato Kugel, Israel J. Math. 40 (1981), 331-339. MR 654588 (83d:31002)
  • [K] O. D. Kellogg, Foundations of potential theory, 4th printing, Ungar, New York, 1970.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1162956-7
Keywords: Single-layer potential, harmonic function, mean value property
Article copyright: © Copyright 1992 American Mathematical Society

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