Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Convexity and the Exterior Inverse Problem of Potential Theory


Authors: Stephen J. Gardiner and Tomas Sjödin
Journal: Proc. Amer. Math. Soc. 136 (2008), 1699-1703
MSC (2000): Primary 31B20
DOI: https://doi.org/10.1090/S0002-9939-07-09228-3
Published electronically: November 30, 2007
MathSciNet review: 2373599
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • 1. D. Aharonov, M. M. Schiffer and L. Zalcman, Potato kugel, Israel J. Math. 40 (1981), 331-339. MR 654588 (83d:31002)
  • 2. D. H. Armitage and S. J. Gardiner, Classical potential theory. Springer Monographs in Mathematics. Springer, London, 2001. MR 1801253 (2001m:31001)
  • 3. B. Gustafsson, On quadrature domains and an inverse problem in potential theory, J. Analyse Math. 55 (1990), 172-216. MR 1094715 (92c:31013)
  • 4. B. Gustafsson and M. Sakai, Properties of some balayage operators, with applications to quadrature domains and moving boundary problems, Nonlinear Anal. 22 (1994), 1221-1245. MR 1279981 (95h:31007)
  • 5. 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.
  • 6. P. S. Novikoff, Sur le problème inverse du potentiel, C. R. (Dokl.) Acad. Sci. URSS (N.S.) 18 (1938), 165-168.
  • 7. H. Shahgholian, Convexity and uniqueness in an inverse problem of potential theory, Proc. Amer. Math. Soc. 116 (1992), 1097-1100. MR 1137234 (93b:31008)
  • 8. T. Sjödin, On the structure of partial balayage, Nonlinear Anal. 67 (2007), 94-102. MR 2313881
  • 9. L. Zalcman, Some inverse problems of potential theory, Integral geometry (Brunswick, Maine, 1984), pp. 337-350, Contemp. Math., 63, Amer. Math. Soc., Providence, RI, 1987. MR 876329 (88e:31012)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 31B20

Retrieve articles in all journals with MSC (2000): 31B20


Additional Information

Stephen J. Gardiner
Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: stephen.gardiner@ucd.ie

Tomas Sjödin
Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: tomas.sjodin@ucd.ie

DOI: https://doi.org/10.1090/S0002-9939-07-09228-3
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society