# A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction

Yves Capdeboscq; Michael S. Vogelius

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 1, page 159-173
- ISSN: 0764-583X

## Access Full Article

top## Abstract

top## How to cite

topCapdeboscq, Yves, and Vogelius, Michael S.. "A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction." ESAIM: Mathematical Modelling and Numerical Analysis 37.1 (2010): 159-173. <http://eudml.org/doc/194151>.

@article{Capdeboscq2010,

abstract = {
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.
},

author = {Capdeboscq, Yves, Vogelius, Michael S.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Voltage perturbations; conductivity inhomogeneities; low volume fraction.; voltage perturbations; low volume fraction},

language = {eng},

month = {3},

number = {1},

pages = {159-173},

publisher = {EDP Sciences},

title = {A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction},

url = {http://eudml.org/doc/194151},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Capdeboscq, Yves

AU - Vogelius, Michael S.

TI - A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 1

SP - 159

EP - 173

AB -
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.

LA - eng

KW - Voltage perturbations; conductivity inhomogeneities; low volume fraction.; voltage perturbations; low volume fraction

UR - http://eudml.org/doc/194151

ER -

## References

top- 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
- 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). Zbl1036.35050
- H. Ammari and J.K. Seo, A new formula for the reconstruction of conductivity inhomogeneities. Preprint (2002). Zbl1040.78008
- 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. Zbl1075.78010
- 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. Zbl0974.78006
- 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). Zbl1089.78003
- M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. (to appear). Zbl1016.65079
- 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). Zbl1137.35347
- 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 Problems14 (1998) 553-595. Zbl0916.35132
- 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. Zbl0684.35087
- 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). Zbl0562.35001
- 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
- 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
- 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). Zbl0846.60081

## Citations in EuDML Documents

top- Hoai-Minh Nguyen, Michael S. Vogelius, A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity
- Yves Capdeboscq, Michael S. Vogelius, Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
- Yves Capdeboscq, Michael S. Vogelius, Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
- Roland Griesmaier, A general perturbation formula for electromagnetic fields in presence of low volume scatterers
- Roland Griesmaier, A general perturbation formula for electromagnetic fields in presence of low volume scatterers
- Habib Ammari, Hyeonbae Kang, Sur le Problème de Conductivité Inverse
- Stanislas Larnier, Mohamed Masmoudi, The extended adjoint method
- Stanislas Larnier, Mohamed Masmoudi, The extended adjoint method

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.