Optimal size estimates for the inverse conductivity problem with one measurement
Authors:
G. Alessandrini, E. Rosset and J. K. Seo
Journal:
Proc. Amer. Math. Soc. 128 (2000), 5364
MSC (2000):
Primary 31B20; Secondary 35R25, 35R30, 35R05
Published electronically:
September 9, 1999
MathSciNet review:
1695112
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We prove upper and lower estimates on the measure of an inclusion in a conductor in terms of one pair of current and potential boundary measurements. The growth rates of such estimates are essentially best possible.
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 G. Alessandrini and E. Rosset, The inverse conductivity problem with one measurement: bounds on the size of the unknown object, SIAM J. Appl. Math. 58, 4 (1998), 10601071. CMP 98:12
 [BF]
 H. Bellout and A. Friedman, Identification problems in potential theory, Arch. Rational Mech. Anal. 101 (1988), 143160. MR 90g:31005
 [BFI]
 H. Bellout, A. Friedman, and V. Isakov, Stability for an inverse problem in potential theory, Trans. Amer. Math. Soc. 332 (1992), 271296. MR 92j:31010
 [BFS]
 B. Barceló, E. Fabes, and J. K. Seo, The inverse conductivity problem with one measurement: uniqueness for convex polyhedra, Proc. Amer. Math. Soc. 122 (1994), 183189. MR 94k:35320
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Additional Information
G. Alessandrini
Affiliation:
Dipartimento di Scienze Matematiche, Università Degli Studi di Trieste, 34100 Trieste, Italy
Email:
alessang@univ.trieste.it
E. Rosset
Email:
rossedi@univ.trieste.it
J. K. Seo
Affiliation:
Department of Mathematics, Yonsey University, Seoul 120749, Korea
Email:
seoj@bubble.yonsei.ac.kr
DOI:
http://dx.doi.org/10.1090/S000299399905474X
PII:
S 00029939(99)05474X
Keywords:
Inverse conductivity problem,
size estimates,
Muckenhoupt weights
Received by editor(s):
February 11, 1998
Published electronically:
September 9, 1999
Additional Notes:
This research was supported in part by Fondi MURST 40% and 60% and by CNR
Communicated by:
Lesley M. Sibner
Article copyright:
© Copyright 1999
American Mathematical Society
