The electromagnetic interior transmission problem for regions with cavities

SIAM Journal on Mathematical Analysis

Volumn 43, Issue 4, 2011, Pages 1698-1715

  Cossonnière, Anne ^a   Haddar, Houssem ^b  

^a CERFACS   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Inhomogeneous medium; Interior transmission problem; Transmission eigenvalues

Indexed keywords

DISCRETE SETS; EIGEN-VALUE; EIGENVALUES; ELECTRIC PERMITTIVITIES; ELECTROMAGNETIC PERMEABILITY; FOURTH ORDER; FREDHOLM; HOST MEDIUMS; INDEX OF REFRACTION; INHOMOGENEOUS MEDIUM; INTERIOR TRANSMISSION PROBLEM; INTERIOR TRANSMISSION PROBLEMS; MONOTONICITY PROPERTY;

EIGENVALUES AND EIGENFUNCTIONS; MAGNETIC PERMEABILITY; PERMITTIVITY; REFRACTIVE INDEX;

ELECTROMAGNETISM;

EID: 80052742652     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/100813890     Document Type: Article

References (13)

1. F. CAKONI and D. COLTON, Qualitative Methods in Inverse Scattering Theory: An Introduction, Interact. Mech. Math., Springer-Verlag, Berlin, 2006.
2. F. CAKONI, D. COLTON, and H. HADDAR, The computation of lower bounds for the norm of the index of refraction in an anisotropic media, J. Integral Equations Appl., 21(2009), pp. 203-227.
3. F. CAKONI, D. COLTON, and H. HADDAR, The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42(2010), pp. 145-162.
4. F. CAKONI, D. COLTON, and P. MONK, On the use of transmission eigenvalues to estimate the index of refraction from far field data, Inverse Problems, 23(2007), pp. 507-522. (Pubitemid 46453820)
5. F. CAKONI, D. GINTIDES, and H. HADDAR, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42(2010), pp. 237-255.
6. F. CAKONI and H. HADDAR, On the existence of transmission eigenvalues in an inhomogeneous medium, Appl. Anal., 88(2008), pp. 475-493.
7. D. COLTON and R. KRESS, Inverse Acoustic and Electromagnetic Scattering Theory, 22nd ed., Springer-Verlag, New York, 1998.
8. D. COLTON, L. PÄIVÄRINTA, and J. SYLVESTER, The interior transmission problem, Inverse Probl. Imaging, 1(2007), pp. 13-28.
9. R. DAUTRAY and J.-L. LIONS, Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 3. Spectral Theory and Applications, Springer-Verlag, Berlin, 1990.
10. H. HADDAR, The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem, Math. Methods Appl. Sci., 27(2004), pp. 2111-2129.
11. A. KIRSCH and N. GRINBERG, The Factorization Method for Inverse Problems, Oxford Lecture Ser. Math. Appl. 36, Oxford University Press, Oxford, 2008.
12. L. PÄIVÄRINTA and J. SYLVESTER, Transmission eigenvalues, SIAM J. Math. Anal., 40(2008), pp. 738-753.
13. N. WECK, Approximation by Maxwell-Herglotz-fields, Math. Methods Appl. Sci., 27(2004), pp. 603-621.