## diameter by boundary measurements

### BibTeX

@MISC{Moskow_diameterby,

author = {D. J. Cedio-fengya S. Moskow},

title = {diameter by boundary measurements},

year = {}

}

### OpenURL

### Abstract

Identi cation of conductivity imperfections of small

### Citations

210 |
Linear integral equations
- Kress
- 1999
(Show Context)
Citation Context ...e existence of v is most easily established by representing it as a single layer potential on @B for a suitably chosen smooth density (that solves an associated boundary integral equation, cf. [5] or =-=[11]-=-). A single layer potential always vanishes at in nity for n 3, for n = 2 the vanishing at in nity of this particular representation relies on the fact that R @B rxU(0) y d y = 0. A maximum principle ... |

178 |
A global uniqueness theorem for an inverse boundary value problem
- Sylvester, Uhlmann
- 1987
(Show Context)
Citation Context ... Introduction The non-destructive inspection technique known as electrical impedance imaging has recently received considerable attention in the mathematical- as well as in the engineering literature =-=[2, 4, 10, 14,17]-=-. Using this technique one seeks to determine information about the internal conductivity- (or impedance) prole of an object based on boundary information about the applied steady-state currents and c... |

116 |
Global uniqueness for a two-dimensional inverse boundary value problem
- Nachman
- 1996
(Show Context)
Citation Context ... Introduction The non-destructive inspection technique known as electrical impedance imaging has recently received considerable attention in the mathematical- as well as in the engineering literature =-=[2, 4, 10, 14,17]-=-. Using this technique one seeks to determine information about the internal conductivity- (or impedance) prole of an object based on boundary information about the applied steady-state currents and c... |

57 |
Determining conductivity by boundary measurements
- Kohn, Vogelius
- 1985
(Show Context)
Citation Context ... Introduction The non-destructive inspection technique known as electrical impedance imaging has recently received considerable attention in the mathematical- as well as in the engineering literature =-=[2, 4, 10, 14,17]-=-. Using this technique one seeks to determine information about the internal conductivity- (or impedance) prole of an object based on boundary information about the applied steady-state currents and c... |

18 |
On the uniqueness in the inverse conductivity problem with one measurement
- Friedman, Isakov
- 1989
(Show Context)
Citation Context ... University, New Brunswick, NJ 08903, USA 1features. Examples of the latter type are found in connection with the identication of cracks [12, 15] and the identi cation of one or more inhomogeneities =-=[1, 6, 7, 8]-=-. Following this line of investigation the purpose of the present paper is to design an e cient method to determine the location and size of diametrically small conductivity imperfections inside a con... |

13 |
A boundary integral equation method for an inverse problem related to crack detection
- Nishimura, Kobayashi
- 1991
(Show Context)
Citation Context ...ta, Minneapolis, MN 55455 z Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA 1features. Examples of the latter type are found in connection with the identication of cracks =-=[12, 15]-=- and the identi cation of one or more inhomogeneities [1, 6, 7, 8]. Following this line of investigation the purpose of the present paper is to design an e cient method to determine the location and s... |

10 |
Introduction to Partial Di erential Equations
- Folland
- 1976
(Show Context)
Citation Context ...yj!1 The existence of v is most easily established by representing it as a single layer potential on @B for a suitably chosen smooth density (that solves an associated boundary integral equation, cf. =-=[5]-=- or [11]). A single layer potential always vanishes at in nity for n 3, for n = 2 the vanishing at in nity of this particular representation relies on the fact that R @B rxU(0) y d y = 0. A maximum pr... |

9 |
Progress in electrical impedance tomography
- Brown, Barber
- 1990
(Show Context)
Citation Context |

8 |
M.: Crack determination from boundary measurements reconstruction using experimental data
- Liepa, Santosa, et al.
- 1993
(Show Context)
Citation Context ...ta, Minneapolis, MN 55455 z Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA 1features. Examples of the latter type are found in connection with the identication of cracks =-=[12, 15]-=- and the identi cation of one or more inhomogeneities [1, 6, 7, 8]. Following this line of investigation the purpose of the present paper is to design an e cient method to determine the location and s... |

5 |
Stabilized numerical analytic prolongation with poles
- Miller
- 1970
(Show Context)
Citation Context ...the proof of an almost identical result) we refer the reader to [7]. Let us also note that for n = 2 and = @ there is a close relation between Theorem 3 and the continuous dependence results found in =-=[13]-=-. Sketch of the main ideas of proof By combining the representation formula (54) with the fact that Mi = n i M( (zi)=k), where M(r) is the rescaled polarization tensor associated with B and conductivi... |

3 | Layer potential theory for the inverse conductivity problem - Kang, Seo - 1996 |

1 | An algorithm for solving the inverse conductivity problem - Cedio-Fengya, Thesis - 1997 |

1 |
Identi cation of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence
- Friedman, Vogelius
- 1989
(Show Context)
Citation Context ... University, New Brunswick, NJ 08903, USA 1features. Examples of the latter type are found in connection with the identication of cracks [12, 15] and the identi cation of one or more inhomogeneities =-=[1, 6, 7, 8]-=-. Following this line of investigation the purpose of the present paper is to design an e cient method to determine the location and size of diametrically small conductivity imperfections inside a con... |

1 |
Virtual mass and polarization
- er, M, et al.
- 1949
(Show Context)
Citation Context ... tend towards 0 or 1 in the approximation obtained here. Polarization tensors corresponding to these two extreme cases have been considered many other places in the literature; we refer the reader to =-=[16]-=- and [9]. 2 266.1 The limit as k ! 0. Let (k) j 2 C(<n ); j =1; :::; n; denote the unique solutions to 4 (k) j =0; in B ; 4 (k) j =0; in <n nB (k) j @ (k) + j @ is continuous across @B lim jyj!1 k @ ... |