Volume 37, Number 1, January/February 2003
|Page(s)||159 - 173|
|Published online||15 March 2003|
- 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. [CrossRef] [MathSciNet]
- H. Ammari and H. Kang, High-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of conductivity inhomogeneities of small diameter. Preprint (2002).
- H. Ammari and J.K. Seo, A new formula for the reconstruction of conductivity inhomogeneities. Preprint (2002).
- H. Ammari, S. Moskow and M.S. Vogelius, Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. ESAIM Control Optim. Calc. Var. 9 (2003) 49-66. [CrossRef] [EDP Sciences] [MathSciNet]
- E. Beretta, A. Mukherjee and M.S. Vogelius, Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. Z. Angew. Math. Phys. 52 (2001) 543-572. [CrossRef] [MathSciNet]
- 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).
- M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. (to appear).
- Y. Capdeboscq and M.S. Vogelius, Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements. ESAIM: M2AN (to appear).
- 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. [CrossRef] [MathSciNet]
- A. Friedman and M.S. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence. Arch. Ration. Mech. Anal. 105 (1989) 299-326. [CrossRef] [MathSciNet]
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Grundlehren der mathematischen Wissenschaften, Vol. 224. Springer-Verlag, Berlin, Heidelberg, New York (1983).
- 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. [CrossRef] [MathSciNet]
- 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. [CrossRef] [MathSciNet]
- F. Murat and L. Tartar, H-Convergence, in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R.V. Kohn Eds., Progress in Nonlinear Differential Equations and Their Applications, Vol. 31, pp. 21-43. Birkhäuser, Boston, Basel, Berlin (1997).
- G.C. Papanicolaou, Diffusion in random media, Surveys in Applied Mathematics, Vol. 1, Chap. 3, J.B. Keller, D.W. Mclaughlin and G.C. Papanicolaou Eds., Plenum Press, New York (1995).
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