A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity

Hoai-Minh Nguyen; Michael S. Vogelius

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 6, page 2283-2315
  • ISSN: 0294-1449

How to cite

top

Nguyen, Hoai-Minh, and 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 26.6 (2009): 2283-2315. <http://eudml.org/doc/78934>.

@article{Nguyen2009,
author = {Nguyen, Hoai-Minh, Vogelius, Michael S.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {voltage representation formulas; small inhomogeneities; cloaking},
language = {eng},
number = {6},
pages = {2283-2315},
publisher = {Elsevier},
title = {A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity},
url = {http://eudml.org/doc/78934},
volume = {26},
year = {2009},
}

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
PB - Elsevier
VL - 26
IS - 6
SP - 2283
EP - 2315
LA - eng
KW - voltage representation formulas; small inhomogeneities; cloaking
UR - http://eudml.org/doc/78934
ER -

References

top
  1. [1] Ammari H., Kang H., Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Math., vol. 1846, Springer-Verlag, 2004. Zbl1113.35148MR2168949
  2. [2] Astala K., Päivärinta L., Calderón's inverse conductivity problem in the plane, Ann. of Math.163 (2006) 265-299. Zbl1111.35004MR2195135
  3. [3] Brühl M., Hanke M., Vogelius M.S., A direct impedance tomography algorithm for locating small inhomogeneities, Numer. Math.93 (2003) 635-654. Zbl1016.65079MR1961882
  4. [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. Zbl1137.35346MR1972656
  5. [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 Problems14 (1998) 553-595. Zbl0916.35132MR1629995
  6. [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. Zbl0684.35087MR973245
  7. [7] Greenleaf A., Lassas M., Uhlmann G., On nonuniqueness for Calderon's inverse problem, Math. Res. Lett.10 (2003) 685-693. Zbl1054.35127MR2024725
  8. [8] Greenleaf A., Lassas M., Uhlmann G., Anisotropic conductivities that cannot be detected by EIT, Physiological Meas.24 (2003) 413-419. 
  9. [9] Kohn R.V., Shen H., Vogelius M.S., Weinstein M.I., Cloaking via change of variables in Electrical Impedance Tomography, Inverse Problems24 (2008) 015016, (21 pp). Zbl1153.35406MR2384775
  10. [10] Kohn R.V., Vogelius M., Determining conductivity by boundary measurements II. Interior results, Comm. Pure Appl. Math.38 (1985) 643-667. Zbl0595.35092MR803253
  11. [11] Kohn R.V., Vogelius M., Relaxation of a variational method for impedance computed tomography, Comm. Pure Appl. Math.40 (1987) 745-777. Zbl0659.49009MR910952
  12. [12] Nachman A.I., Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math.143 (1996) 71-96. Zbl0857.35135MR1370758
  13. [13] Nedelec J.-C., Acoustic and Electromagnetic Equations, Appl. Math. Sci., vol. 144, Springer-Verlag, 2001. Zbl0981.35002MR1822275
  14. [14] Pendry J.B., Schurig D., Smith D.R., Controlling electromagnetic fields, Science312 (2006) 1780-1782. Zbl1226.78003MR2237570
  15. [15] Sylvester J., Uhlmann G., A global uniqueness theorem for an inverse boundary value problem, Ann. of Math.125 (1987) 153-169. Zbl0625.35078MR873380

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.