Publication Cover
Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 4
211
Views
89
CrossRef citations to date
0
Altmetric
Original Articles

On the existence of transmission eigenvalues in an inhomogeneous medium

&
Pages 475-493 | Received 24 Dec 2008, Accepted 28 Dec 2008, Published online: 16 Jun 2009

References

  • Cakoni , F , Cayoren , M and Colton , D . 2008 . Transmission eigenvalues and the nondestructive testing of dielectrics . Inverse Probl. , 26 ( 6 ) paper 065016
  • Cakoni , F , Colton , D and Monk , P . 2007 . On the use of transmission eigenvalues to estimate the index of refraction from far field data . Inverse Probl. , 23 : 507 – 522 .
  • Cakoni , F and Colton , D . 2006 . Qualitative Methods in Inverse Scattering Theory , Berlin : Springer .
  • Colton , D and Kress , R . 1989 . Inverse Acoustic and Electromagnetic Scattering Theory, . , 2nd ed , Appl. Math. Sci. Vol. 93 , New York : Springer .
  • Colton , D , Päivärinta , L and Sylvester , J . 2007 . The interior transmission problem . Inverse Probl. Imaging , 1 : 13 – 28 .
  • Colton , D , Kirsch , A and Päivärinta , L . 1989 . Far eld patterns for acoustic waves in an inhomogeneous medium . SIAM J. Math. Anal. , 20 : 1472 – 1483 .
  • Kirsch , A . 2007 . An integral equation approach and the interior transmission problem for Maxwell's equations . Inverse Probl. Imaging , 1 : 159 – 179 .
  • Cakoni , F , Colton , D and Haddar , H . 2002 . The linear sampling method for anisotropic media . J. Comput. Appl. Math. , 146 : 285 – 299 .
  • Cakoni , F and Haddar , H . 2007 . A variational approach for the solution of electromagnetic interior transmission problem for anisotropic media . Inverse Probl. Imaging , 1 ( 3 ) : 443 – 456 .
  • 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 Eq. Appl. 21(2) (2009), pp. 203–227
  • Haddar , H . 2004 . The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem . Math. Methods Appl. Sci. , 27 ( 18 ) : 2111 – 2129 .
  • Rynne , BP and Sleeman , BD . 1992 . The interior transmission problem and inverse scattering from inhomogeneous media . SIAM J. Math. Anal. , 22 : 1755 – 1762 .
  • Päivärinta , L and Sylvester , J . 2008 . Transmission eigenvalues . SIAM J. Math. Anal. , 40 : 738 – 753 .
  • A. Kirsch, On the existence of transmission eigenvalues, Inverse Probl. Imaging 3(2) (2009), pp. 155–172
  • Reed , M and Simon , B . 1980 . Functional Analysis , New York : Academic Press .
  • Nédélec , J-C . 2001 . Acoustic and Electromagnetic Equations , Vol. 144 , New York : Springer . Applied Mathematical Sciences

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.