Stability for an inverse problem in potential theory

Authors:
Hamid Bellout, Avner Friedman and Victor Isakov

Journal:
Trans. Amer. Math. Soc. **332** (1992), 271-296

MSC:
Primary 31B20; Secondary 31B35, 35J25, 35R30

DOI:
https://doi.org/10.1090/S0002-9947-1992-1069743-3

MathSciNet review:
1069743

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Abstract: Let be a subdomain of a bounded domain in . The conductivity coefficient of is a positive constant and the conductivity of is equal to . For a given current density on , we compute the resulting potential and denote by the value of on . The general inverse problem is to estimate the location of from the known measurements of the voltage . If is a family of domains for which the Hausdorff distance equal to ( small), then the corresponding measurements are close to . This paper is concerned with proving the inverse, that is, , ; the domains and are assumed to be piecewise smooth. If , we assume in proving the above result, that (or ) for all small . For this monotonicity condition is dropped, provided is appropriately chosen. The above stability estimate provides quantitative information on the location of by means of .

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1069743-3

Article copyright:
© Copyright 1992
American Mathematical Society