Attainability by simply connected domains of optimal bounds for the polarization tensor

European Journal of Applied Mathematics

Volumn 17, Issue 2, 2006, Pages 201-219

  Ammari, Habib ^a   Capdeboscq, Yves ^b   Kang, Hyeonbae ^c   Kim, Eunjoo ^a   Lim, Mikyoung ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

^c Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749324232     PISSN: 09567925     EISSN: 14694425     Source Type: Journal    
DOI: 10.1017/S0956792506006541     Document Type: Article

References (22)

1. AMMARI, H. & KANG, H. (2004) Reconstruction of Small Inhomogeneities from Boundary Measurements. Lecture Notes in Math. 1846, Springer-Verlag.
2. AMMARI, H. & KANG, H. (2003) High-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of conductivity inhomogeneities of small diameter. SIAM J. Math. Anal. 34, 1152-1166.
3. AMMARI, H. & KANG, H. (2003) Properties of the generalized polarization tensors, Multiscale Modeling and Simulation: A SIAM Interdisciplinary J. 1, 335-348.
4. AMMARI, H., KANG, H. & KIM, K. (2005) Anisotropic polarization tensors and effective properties of anisotropic composite materials. J. Diff. Equal. 215, 401-428.
5. AMMARI, H., KANG, H., KIM, E. & LIM, M. (2005) Reconstruction of closely spaced small inclusions. SIAM J. Numer. Anal. 42, 2408-2428.
6. AMMARI, H., KANG, H. & TOUIBI, K. (2005) Boundary layer techniques for deriving the effective properties of composite materials. Asymp. Anal. 41, 119-140.
7. BERETTA, E., FRANCINI, E. & VOGELIUS, M. S. (2003) Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis. J. Math. Pures Appl. 82, 1277-1301.
8. BRÜHL, M., HANKE, M. & VOGELIUS, M. S. (2003) A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. 93, 635-654.
9. CAPDEBOSCQ, Y. & KANG, H. (n.d.) Improved Hashin-Shtrikman bound for thick domains. Contemporary Math. (to appear).
10. CAPDEBOSCQ, Y. & VOGELIUS, M. S. (2003) A general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction, Math. Modelling Num. Anal. 37 (2003), pp. 159-173.
11. CAPDEBOSCQ, Y. & VOGELIUS, M. S. (2003) Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements. Math. Modelling Num. Anal. 37, 227-240.
12. CAPDEBOSCQ, Y. & VOGELIUS, M. S. (2003) A review of some recent work on impedance imaging for inhomogneieties of low volume fraction. Proceedings Pan-American Advanced Studies Institute on PDEs, Inverse problems and Nonlinear Analysis.
13. CEDIO-FENGYA, D. J., MOSKOW, S. & VOGELIUS, M. (1998) Identification of conductivity imperfections of small diameter by boundary measurements: Continuous dependence and computational reconstruction. Inverse Problem, 14, 553-595.
14. DASSIOS, G. & KLEINMAN, R. E. (2000) Low Frequency Scattering. Oxford Science Publications. The Clarendon Press, Oxford University Press.
15. JIKOV, V. V., KOZLOV, S. M. & OLEINIK, O. A. (1994) Homogenization of Differential Operators and Integral Functionals. Springer-Verlag.
16. KLEINMAN, R. E. & SENIOR, T. B. A. (1986) Rayleigh scattering. In: V. K. Varadan and V. V. Varadan, editors, Low and High Frequency Asymptotics, pp. 1-70. North-Holland.
17. KOHN, R. V. & MILTON, G. W. (1986) On bounding the effective conductivity of anisotropic composites. Homogenization and Effective Moduli of Materials and Media, IMA Volumes in Mathematics and its Applications 1, pp. 97-125.
18. KRESS, R. (1980) Linear Integral Equations, Applied Mathematical Sciences, Vol. 82, Springer-Verlag.
19. LIPTON, R. (1993) Inequalities for electric and elastic polarization tensors with applications to random composites. J. Mech. Phys. Solids, 41, 809-833.
20. MILTON, G. W. (2001) The Theory of Composites. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press.
21. PÓLYA, G. & SZEGÖ, G. (1951) Isoperimetric Inequalities in Mathematical Physics. Ann. Math. Stud. 27.
22. SHIFFER, M. & SZEGÖ, G. (1949) Virtual mass and polarization. Trans. Amer. Math. Soc. 67, 130-205.