Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
Yves Capdeboscq; Michael S. Vogelius
- Volume: 37, Issue: 2, page 227-240
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] G. Alessandrini, E. Rosset and J.K. Seo, Optimal size estimates for the inverse conductivity problem with one measurement. Proc. Amer. Math. Soc. 128 (2000) 53–64. Zbl0944.35108
- [2] G. Alessandrini, A. Morassi and E. Rosset, Detecting cavities by electrostatic boundary measurements. Preprint (2002). Zbl1010.35117MR1943396
- [3] H. Ammari and J.K. Seo, A new formula for the reconstruction of conductivity inhomogeneities. Preprint (2002). Zbl1040.78008
- [4] H. Ammari, S. Moskow and M.S. Vogelius, Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. ESAIM: Cont. Opt. Calc. Var. 9 (2003) 49–66. Zbl1075.78010
- [5] E. Beretta, E. Francini and M.S. Vogelius, Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis. Preprint (2002). Zbl1089.78003MR2020923
- [6] M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Problems 16 (2000) 1029–1042. Zbl0955.35076
- [7] M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. 93 (2003) 635–654. Zbl1016.65079
- [8] Y. Capdeboscq and M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. ESAIM: M2AN 37 (2003) 159–173. Zbl1137.35346
- [9] D.J. Cedio-Fengya, S. Moskow and M.S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems 14 (1998) 553–595. Zbl0916.35132
- [10] A. Friedman and V. Isakov, On the uniqueness in the inverse conductivity problem with one measurement. Indiana Univ. Math. J. 38 (1989) 553–580. Zbl0703.35165
- [11] S. He and V.G. Romanov, Identification of small flaws in conductors using magnetostatic measurements. Math. Comput. Simulation 50 (1999) 457–471.
- [12] M. Ikehata and T. Ohe, A numerical method for finding the convex hull of polygonal cavities using the enclosure method. Inverse Problems 18 (2002) 111–124. Zbl0992.35118
- [13] H. Kang, J.K. Seo and D. Sheen, The inverse conductivity problem with one measurement: stability and estimation of size. SIAM J. Math. Anal. 28 (1997) 1389–1405. Zbl0888.35131
- [14] R.V. Kohn and G.W. Milton, On bounding the effective conductivity of anisotropic composites, in Homogenization and Effective Moduli of Materials and Media, J.L. Ericksen, D. Kinderlehrer, R. Kohn and J.-L. Lions Eds., Springer-Verlag, IMA Vol. Math. Appl. 1 (1986) 97–125. Zbl0631.73012
- [15] O. Kwon, J.K. Seo and J.-R. Yoon, A real time algorithm for the location search of discontinuous conductivities with one measurement. Comm. Pure Appl. Math. 55 (2002) 1–29. Zbl1032.78005
- [16] R. Lipton, Inequalities for electric and elastic polarization tensors with applications to random composites. J. Mech. Phys. Solids 41 (1993) 809-833. Zbl0797.73046MR1214019