Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter

Michael S. Vogelius; Darko Volkov

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 4, page 723-748
  • ISSN: 0764-583X

How to cite

top

Vogelius, Michael S., and Volkov, Darko. "Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.4 (2000): 723-748. <http://eudml.org/doc/194010>.

@article{Vogelius2000,
author = {Vogelius, Michael S., Volkov, Darko},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Maxwell equations; inhomogeneities of small diameter; asymptotic formulas; identification problems},
language = {eng},
number = {4},
pages = {723-748},
publisher = {Dunod},
title = {Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter},
url = {http://eudml.org/doc/194010},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Vogelius, Michael S.
AU - Volkov, Darko
TI - Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 4
SP - 723
EP - 748
LA - eng
KW - Maxwell equations; inhomogeneities of small diameter; asymptotic formulas; identification problems
UR - http://eudml.org/doc/194010
ER -

References

top
  1. [1] H. Ammari, S. Moskow and M. Vogelius, Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter. Preprint, Rutgers University (1999); Inverse Problems (submitted). Zbl1075.78010
  2. [2] P.M. Anselone, Collectively Compact Operator Approximation Theory and Applications to Integral Equations. Prentice-Hall, Englewood Cliffs, New Jersey (1971). Zbl0228.47001MR443383
  3. [3] L. Baratchart, J. Leblond, F. Mandréa and E.B. Saff, How can meromorhic approximation help to solve some 2D inverse problems for the Laplacian ? Inverse Problems 15 (1999) 79-90. Zbl0921.35187MR1675335
  4. [4] J. Blitz, Electrical and Magnetic Methods of Nondestructive Testing. IOP Publishing, Adam Hilger, New York (1991). 
  5. [5] D. Cedio-Fengya, S. Moskow and M.S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems 14 (1998) 553-595. Zbl0916.35132MR1629995
  6. [6] D. Colton and R. Kress, Integral Equation Methods in Scattering Theory. Krieger Publishing Co., Malabar, Florida (1992). Zbl0522.35001
  7. [7] D. Dobson and F. Santosa, Nondestructive evaluation of plates using eddy current methods. Internat. J. Engrg. Sci. 36 (1998) 395-409. Zbl1210.78010MR1620127
  8. [8] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Ed., Springer-Verlag, New York (1983). Zbl0562.35001MR737190
  9. [9] D. Griffiths, Introduction to Electrodynamics, 2nd Ed., Prentice Hall, Upper Saddle River, New Jersey (1989). 
  10. [10] F. Gylys-Colwell, An inverse problem for the Helmholtz equation. Inverse Problems 12 (1996) 139-156. Zbl0860.35142MR1382235
  11. [11] J.D. Jackson, Classical Electrodynamics, 2nd Ed., Wiley, New York (1975). Zbl0997.78500MR436782
  12. [12] R. Kohn and M. Vogelius, Determining conductivity by boundary measurements. Comm. Pure Appl. Math. 37 (1984) 289-298. II. Interior results. Comm. Pure Appl. Math. 38 (1985) 643-667. Zbl0595.35092MR739921
  13. [13] M. Lassas, The impedance imaging problem as a low-frequency limit. Inverse Problems 13 (1997) 1503-1518. Zbl0903.35090MR1484001
  14. [14] N.N. Lebedev, Special Functions & Their Applications. Dover Publications, New York (1972). Zbl0271.33001MR350075
  15. [15] A. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem. Ann. of Math. 143 (1996) 71-96. Zbl0857.35135MR1370758
  16. [16] P. Ola, L. Päivärinta and E. Somersalo, An inverse boundary value problem in electrodynamics. Duke Math. J. 70 (1993) 617-653. Zbl0804.35152MR1224101
  17. [17] A. Sahin and E.L. Miller, Electromagnetic scattering-based array processing methods for near-field object characterization. Preprint, Northeastern University (1998). Zbl1064.78506
  18. [18] E. Somersalo, D. Isaacson and M. Cheney, A linearized inverse boundary value problem for Maxwell's equations. J. Comput. Appl. Math. 42 (1992) 123-136. Zbl0757.65128MR1181585
  19. [19] J. Sylvester and G. Uhlmann, A uniqueness theorem for an inverse boundary value problem in electrical prospection. Comm. Pure Appl. Math. 39 (1986) 91-112. Zbl0611.35088MR820341
  20. [20] J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. of Math. 125 (1987) 153-169. Zbl0625.35078MR873380
  21. [21] G.N. Watson, A Treatise on the Theory of Bessel Functions, 2nd Ed., Cambridge University Press, London (1962). Zbl0174.36202MR1349110JFM48.0412.02

NotesEmbed ?

top

You must be logged in to post comments.