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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 123, Issue 3
  • January 1993, pp. 497-516

Stable determination of a crack from boundary measurements

  • Giovanni Alessandrini (a1)
  • DOI:
  • Published online: 14 November 2011

We treat the problem of determining a crack inside a conductor when two pairs of current and voltage boundary measurements are given. We prove a theorem of continuous dependence from the data.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1G. Alessandrini . Determining conductivity by boundary measurements: the stability issue. In Applied and Industrial Mathematics, ed. R. Spigler (Dordrecht: Kluwer, 1991).

2E. Beretta and S. Vessella . Stability results for an inverse problem in potential theory. Ann. Mat. Pura Appl. (4) 156 (1990), 381404.

4P. L. Duren and M. M. Schiffer . Robin functions and energy functinals of multiply connected domains. Pacific J. Math. (2) 148 (1991), 251273.

5A. Friedman and M. Vogelius . Determining cracks by boundary measurements. Indiana Univ. Math. J. 38 (1989), 527556.

7V. Isakov . Inverse Source Problems (Providence R.I.; American Mathematical Society, 1990).

9A. Nachman . Reconstruction from boundary measurements. Ann. of Math. 128 (1988), 531576.

11J. Sylvester and G. Uhlmann . A uniqueness theorem for an inverse boundary value problem. Ann. of Math. 125 (1987), 153169.

12F. Santosa and M. Vogelius . A computational algorithm to determine cracks from electrostatic boundary measurements. Internal. J. Engrg. Sci. 29 (1991), 917937.

13J. L. Walsh . The Location of Critical Points of Analytic and Harmonic Functions (New York: American Mathemaical Society, 1950).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
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