Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

 Access to full text

 Full (PDF)

1. [1] H. Ammari, M.S. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell Equations. J. Math. Pures Appl. 80 (2001) 769-814. Zbl1042.78002MR1860816
2. [2] S. Andrieux and A. Ben Abda, Identification of planar cracks by complete overdetermined data: Inversion formulae. Inverse Problems 12 (1996) 553-563. Zbl0858.35131MR1413418
3. [3] S. Andrieux, A. Ben Abda and M. Jaoua, On the inverse emerging plane crack problem. Math. Meth. Appl. Sci. 21 (1998) 895-907. Zbl0916.35129MR1634847
4. [4] H.D. Bui, A. Constantinescu and H. Maigre, Diffraction acoustique inverse de fissure plane : solution explicite pour un solide borné. C. R. Acad. Sci. Paris Sér. II 327 (1999) 971-976. Zbl0966.74038
5. [5] E. Beretta, A. Mukherjee and M. Vogelius, Asymptotic formuli for steady state voltage potentials in the presence of conductivity imperfection of small area. ZAMP 52 (2001) 543-572. Zbl0974.78006MR1856987
6. [6] M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Preprint (2001). Zbl1016.65079MR1961882
7. [7] A.P. Calderon, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics. Soc. Brasileira de Matemática, Rio de Janeiro (1980) 65-73. MR590275
8. [8] D.J. Cedio–Fengya, S. Moskow and M.S. Vogelius, Identification of conductivity inperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems 14 (1998) 553-595. Zbl0916.35132
9. [9] I. Daubechies, Ten Lectures on Wavelets. SIAM, Philadelphia (1992). Zbl0776.42018MR1162107
10. [10] G.B. Folland, Introduction to Partial Differential Equations. Princeton University Press, Princeton (1976). Zbl0325.35001MR599578
11. [11] A. Friedman and M. Vogelius, Identification of Small Inhomogeneities of Extreme Conductivity by Boundary Measurements: A Theorem on Continuous Dependence. Arch. Rational Mech. Anal. 105 (1989) 299-326. Zbl0684.35087MR973245
12. [12] S. He and V.G. Romanov, Identification of small flaws in conductors using magnetostatic measurements. Math. Comput. Simul. 50 (1999) 457-471. MR1768346
13. [13] M.S. Joshi and S.R. McDowall, Total determination of material parameters from electromagnetic boundary information. Pacific J. Math. (to appear). Zbl1012.78012MR1748184
14. [14] K. Miller, Stabilized numerical analytic prolongation with poles. SIAM J. Appl. Math. 18 (1970) 346-363. Zbl0211.19303MR260143
15. [15] P. Ola, L. Païvärinta and E. Somersalo, An inverse boundary value problem in electrodynamics. Duke Math. J. 70 (1993) 617-653. Zbl0804.35152MR1224101
16. [16] M.S. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. ESAIM: M${}^2$AN 34 (2000) 723-748. Zbl0971.78004MR1784483
17. [17] D. Volkov, An inverse problem for the time harmonic Maxwell Equations, Ph.D. Thesis. Rutgers University (2001). 

1. Yves Capdeboscq, Michael S. Vogelius, Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
2. Yves Capdeboscq, Michael S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
3. Yves Capdeboscq, Michael S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
4. Yves Capdeboscq, Michael S. Vogelius, Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
5. Roland Griesmaier, A general perturbation formula for electromagnetic fields in presence of low volume scatterers
6. Roland Griesmaier, A general perturbation formula for electromagnetic fields in presence of low volume scatterers
7. Habib Ammari, Hyeonbae Kang, Sur le Problème de Conductivité Inverse
8. Stanislas Larnier, Mohamed Masmoudi, The extended adjoint method
9. Stanislas Larnier, Mohamed Masmoudi, The extended adjoint method