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 and be bounded solid domains such that their associated volume potentials agree outside . Under the assumption that one of the domains is convex, it is deduced that .

**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)**

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.