A Representation Formula for the Voltage Perturbations Caused by Diametrically Small Conductivity Inhomogeneities. Proof of Uniform Validity
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2283-2315.
@article{AIHPC_2009__26_6_2283_0,
     author = {Nguyen, Hoai-Minh and Vogelius, Michael S.},
     title = {A {Representation} {Formula} for the {Voltage} {Perturbations} {Caused} by {Diametrically} {Small} {Conductivity} {Inhomogeneities.} {Proof} of {Uniform} {Validity}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2283--2315},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.03.005},
     mrnumber = {2569895},
     zbl = {1178.35357},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.005/}
}
TY  - JOUR
AU  - Nguyen, Hoai-Minh
AU  - Vogelius, Michael S.
TI  - A Representation Formula for the Voltage Perturbations Caused by Diametrically Small Conductivity Inhomogeneities. Proof of Uniform Validity
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2283
EP  - 2315
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.005/
DO  - 10.1016/j.anihpc.2009.03.005
LA  - en
ID  - AIHPC_2009__26_6_2283_0
ER  - 
%0 Journal Article
%A Nguyen, Hoai-Minh
%A Vogelius, Michael S.
%T A Representation Formula for the Voltage Perturbations Caused by Diametrically Small Conductivity Inhomogeneities. Proof of Uniform Validity
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2283-2315
%V 26
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.005/
%R 10.1016/j.anihpc.2009.03.005
%G en
%F AIHPC_2009__26_6_2283_0
Nguyen, Hoai-Minh; Vogelius, Michael S. A Representation Formula for the Voltage Perturbations Caused by Diametrically Small Conductivity Inhomogeneities. Proof of Uniform Validity. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2283-2315. doi : 10.1016/j.anihpc.2009.03.005. http://www.numdam.org/articles/10.1016/j.anihpc.2009.03.005/

[1] Ammari H., Kang H., Reconstruction of Small Inhomogeneities From Boundary Measurements, Lecture Notes in Math., vol. 1846, Springer-Verlag, 2004. | MR | Zbl

[2] Astala K., Päivärinta L., Calderón's Inverse Conductivity Problem in the Plane, Ann. of Math. 163 (2006) 265-299. | MR | Zbl

[3] Brühl M., Hanke M., Vogelius M. S., A Direct Impedance Tomography Algorithm for Locating Small Inhomogeneities, Numer. Math. 93 (2003) 635-654. | MR | Zbl

[4] Capdeboscq Y., Vogelius M. S., A General Representation Formula for Boundary Voltage Perturbations Caused by Internal Conductivity Inhomogeneities of Low Volume Fraction, Math. Model. Numer. Anal. 37 (2003) 159-173. | Numdam | MR | Zbl

[5] Cedio-Fengya D. J., Moskow S., Vogelius M. S., Identification of Conductivity Imperfections of Small Diameter by Boundary Measurements. Continuous Dependence and Computational Reconstruction, Inverse Problems 14 (1998) 553-595. | MR | Zbl

[6] Friedman A., Vogelius M., Identification of Small Inhomogeneities of Extreme Conductivity by Boundary Measurements: a Theorem on Continuous Dependence, Arch. Ration. Mech. Anal. 105 (1989) 299-326. | MR | Zbl

[7] Greenleaf A., Lassas M., Uhlmann G., On Nonuniqueness for Calderon's Inverse Problem, Math. Res. Lett. 10 (2003) 685-693. | MR | Zbl

[8] Greenleaf A., Lassas M., Uhlmann G., Anisotropic Conductivities That Cannot Be Detected by EIT, Physiological Meas. 24 (2003) 413-419.

[9] Kohn R. V., Shen H., Vogelius M. S., Weinstein M. I., Cloaking Via Change of Variables in Electrical Impedance Tomography, Inverse Problems 24 (2008) 015016, (21 pp). | MR | Zbl

[10] Kohn R. V., Vogelius M., Determining Conductivity by Boundary Measurements II. Interior Results, Comm. Pure Appl. Math. 38 (1985) 643-667. | MR | Zbl

[11] Kohn R. V., Vogelius M., Relaxation of a Variational Method for Impedance Computed Tomography, Comm. Pure Appl. Math. 40 (1987) 745-777. | MR | Zbl

[12] Nachman A. I., Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, Ann. of Math. 143 (1996) 71-96. | MR | Zbl

[13] Nedelec J.-C., Acoustic and Electromagnetic Equations, Appl. Math. Sci., vol. 144, Springer-Verlag, 2001. | MR | Zbl

[14] Pendry J. B., Schurig D., Smith D. R., Controlling Electromagnetic Fields, Science 312 (2006) 1780-1782. | MR

[15] Sylvester J., Uhlmann G., A Global Uniqueness Theorem for an Inverse Boundary Value Problem, Ann. of Math. 125 (1987) 153-169. | MR | Zbl

Cité par Sources :