no. 1
A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 159-173.

We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.

DOI : 10.1051/m2an:2003014
Classification : 35J20, 35B27, 35R30
Mots clés : voltage perturbations, conductivity inhomogeneities, low volume fraction 
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     author = {Capdeboscq, Yves and Vogelius, Michael S.},
     title = {A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {159--173},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {1},
     year = {2003},
     doi = {10.1051/m2an:2003014},
     mrnumber = {1972656},
     zbl = {1137.35346},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2003014/}
}
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Capdeboscq, Yves; Vogelius, Michael S. A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 159-173. doi : 10.1051/m2an:2003014. http://www.numdam.org/articles/10.1051/m2an:2003014/

[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. | Zbl

[2] 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). | MR | Zbl

[3] H. Ammari and J.K. Seo, A new formula for the reconstruction of conductivity inhomogeneities. Preprint (2002).

[4] 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. | Numdam | Zbl

[5] 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. | Zbl

[6] 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). | MR | Zbl

[7] M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. (to appear). | MR | Zbl

[8] 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). | Numdam | MR | Zbl

[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. | Zbl

[10] 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. | Zbl

[11] 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). | MR | Zbl

[12] 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. | Zbl

[13] 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. | Zbl

[14] 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). | Zbl

[15] 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). | MR | Zbl

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