Convexity and the Exterior Inverse Problem of Potential Theory
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- by Stephen J. Gardiner and Tomas Sjödin PDF
- Proc. Amer. Math. Soc. 136 (2008), 1699-1703 Request permission
Abstract:
Let $\Omega _{1}$ and $\Omega _{2}$ be bounded solid domains such that their associated volume potentials agree outside $\Omega _{1}\cup \Omega _{2}$. Under the assumption that one of the domains is convex, it is deduced that $\Omega _{1}=\Omega _{2}$.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
- David H. Armitage and Stephen J. Gardiner, Classical potential theory, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2001. MR 1801253, DOI 10.1007/978-1-4471-0233-5
- Björn Gustafsson, On quadrature domains and an inverse problem in potential theory, J. Analyse Math. 55 (1990), 172–216. MR 1094715, DOI 10.1007/BF02789201
- Björn Gustafsson and Makoto Sakai, Properties of some balayage operators, with applications to quadrature domains and moving boundary problems, Nonlinear Anal. 22 (1994), no. 10, 1221–1245. MR 1279981, DOI 10.1016/0362-546X(94)90107-4
- A. V. Kondraškov, On the uniqueness of the reconstruction of certain regions from their exterior gravitational potentials (Russian) Ill-posed Mathematical Problems and Problems of Mathematical Geophysics, Novosibirsk (1976), pp. 122-129.
- P. S. Novikoff, Sur le problème inverse du potentiel, C. R. (Dokl.) Acad. Sci. URSS (N.S.) 18 (1938), 165-168.
- Henrik Shahgholian, Convexity and uniqueness in an inverse problem of potential theory, Proc. Amer. Math. Soc. 116 (1992), no. 4, 1097–1100. MR 1137234, DOI 10.1090/S0002-9939-1992-1137234-2
- Tomas Sjödin, On the structure of partial balayage, Nonlinear Anal. 67 (2007), no. 1, 94–102. MR 2313881, DOI 10.1016/j.na.2006.05.001
- Lawrence Zalcman, Some inverse problems of potential theory, Integral geometry (Brunswick, Maine, 1984) Contemp. Math., vol. 63, Amer. Math. Soc., Providence, RI, 1987, pp. 337–350. MR 876329, DOI 10.1090/conm/063/876329
Additional Information
- Stephen J. Gardiner
- Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
- MR Author ID: 71385
- ORCID: 0000-0002-4207-8370
- Email: stephen.gardiner@ucd.ie
- Tomas Sjödin
- Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
- Email: tomas.sjodin@ucd.ie
- Received by editor(s): February 19, 2007
- Published electronically: November 30, 2007
- Additional Notes: This research was supported by Science Foundation Ireland under Grant 06/RFP/MAT057
- Communicated by: Juha M. Heinonen
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1699-1703
- MSC (2000): Primary 31B20
- DOI: https://doi.org/10.1090/S0002-9939-07-09228-3
- MathSciNet review: 2373599