A Representation Formula for the Voltage Perturbations Caused by Diametrically Small Conductivity Inhomogeneities. Proof of Uniform Validity
Annales de l'Institut Henri Poincaré. C, 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'Institut Henri Poincar\'e. C, Analyse non lin\'eaire},
     pages = {2283--2315},
     year = {2009},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     doi = {10.1016/j.anihpc.2009.03.005},
     mrnumber = {2569895},
     zbl = {1178.35357},
     language = {en},
     url = {https://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'Institut Henri Poincaré. C, Analyse non linéaire
PY  - 2009
SP  - 2283
EP  - 2315
VL  - 26
IS  - 6
PB  - Elsevier
UR  - https://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'Institut Henri Poincaré. C, Analyse non linéaire
%D 2009
%P 2283-2315
%V 26
%N 6
%I Elsevier
%U https://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'Institut Henri Poincaré. C, Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2283-2315. doi: 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. | Zbl | MR

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

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

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

[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. | Zbl | MR

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

[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). | Zbl | MR

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

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

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

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

[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. | Zbl | MR

Cité par Sources :