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Transmission eigenvalues for inhomogeneous media containing obstacles
1. | Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553, United States |
2. | CERFACS, 42 avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France |
3. | INRIA Saclay Ile de France/CMAP Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France |
References:
[1] |
A. S. Bonnet-BenDhia, L. Chesnel and H. Haddar, On the use of t-coercivity to study the interior transmission eigenvalue problem, C. R. Acad. Sci., Ser. I, 340 (2011). |
[2] |
A. S. Bonnet-BenDhia, P. Ciarlet and C. Maria Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients, J. Comput. Appl. Math, 234 (2010), 1912-1919.
doi: 10.1016/j.cam.2009.08.041. |
[3] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory," Interaction of Mechanics and Mathematics. Springer-Verlag, Berlin, 2006. |
[4] |
F. Cakoni, D. Colton and D. Gintides, The interior transmission eigenvalue problem, SIAM J. Math. Anal., 42 (2010), 2912-2921.
doi: 10.1137/100793542. |
[5] |
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 and Applications, 21 (2009), 203-227.
doi: 10.1216/JIE-2009-21-2-203. |
[6] |
F. Cakoni, D. Colton and H. Haddar, The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42 (2010), 145-162.
doi: 10.1137/090754637. |
[7] |
F. Cakoni, D. Colton and H. Haddar, On the determination of dirichlet or transmission eigenvalues from far field data, C. R. Acad. Sci. Paris, 348 (2010), 379-383.
doi: 10.1016/j.crma.2010.02.003. |
[8] |
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), 507-522.
doi: 10.1088/0266-5611/23/2/004. |
[9] |
F. Cakoni and D. Gintides, New results on transmission eigenvalues, Inverse Problems and Imaging, 4 (2010), 39-48.
doi: 10.3934/ipi.2010.4.39. |
[10] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255.
doi: 10.1137/090769338. |
[11] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium, Applicable Analysis, 88 (2008), 475-493.
doi: 10.1080/00036810802713966. |
[12] |
F. Cakoni and A. Kirsch, On the interior transmission eigenvalue problem, Int. Jour. Comp. Sci. Math, 3 (2010), 142-167. |
[13] |
D. Colton and R. Kress, "Inverse Acoustic and Eletromagnetic Scattering Theory," Springer, New York, 2nd edition, 1998. |
[14] |
D. Colton, L. Päivärinta and J.Sylvester, The interior transmission problem, Inverse Problems and Imaging, 1 (2007), 13-28.
doi: 10.3934/ipi.2007.1.13. |
[15] |
A. Cossonniere and H. Haddar, The electromagnetic interior transmission problem for regions with cavities, SIAM J. Math. Anal., 43 (2011), 1698-1715.
doi: 10.1137/100813890. |
[16] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, Transmission eigenvalues for operators with constant coefficients, SIAM J. Math. Analysis, 42 (2010), 619-651.
doi: 10.1137/100793748. |
[17] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, Transmission eigenvalues for operators with constant coefficients, Math Research Letters, 18 (2011), 279-293. |
[18] |
A. Kirsch, On the existence of transmission eigenvalues, Inverse Problems and Imaging, 3 (2009), 155-172. |
[19] |
A. Kirsch and N. Grinberg, The factorization method for inverse problems, in "Mathematics and its Applications," Oxford Lecture Series, 36, Oxford University Press, Oxford, 2008. |
[20] |
A. Kirsch and L. Päivärinta, On recovering obstacles inside inhomogeneities, Math. Meth. Appl. Sci., 21 (1998), 2965-2986.
doi: 10.1002/(SICI)1099-1476(19980510)21:7<619::AID-MMA940>3.0.CO;2-P. |
[21] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), 738-753.
doi: 10.1137/070697525. |
[22] |
J. Sylvester, Discreteness of transmission eigenvalues via upper triangular compact operators, SIAM J. Math. Anal., 44 (2012), 341-354.
doi: 10.1137/110836420. |
show all references
References:
[1] |
A. S. Bonnet-BenDhia, L. Chesnel and H. Haddar, On the use of t-coercivity to study the interior transmission eigenvalue problem, C. R. Acad. Sci., Ser. I, 340 (2011). |
[2] |
A. S. Bonnet-BenDhia, P. Ciarlet and C. Maria Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients, J. Comput. Appl. Math, 234 (2010), 1912-1919.
doi: 10.1016/j.cam.2009.08.041. |
[3] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory," Interaction of Mechanics and Mathematics. Springer-Verlag, Berlin, 2006. |
[4] |
F. Cakoni, D. Colton and D. Gintides, The interior transmission eigenvalue problem, SIAM J. Math. Anal., 42 (2010), 2912-2921.
doi: 10.1137/100793542. |
[5] |
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 and Applications, 21 (2009), 203-227.
doi: 10.1216/JIE-2009-21-2-203. |
[6] |
F. Cakoni, D. Colton and H. Haddar, The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42 (2010), 145-162.
doi: 10.1137/090754637. |
[7] |
F. Cakoni, D. Colton and H. Haddar, On the determination of dirichlet or transmission eigenvalues from far field data, C. R. Acad. Sci. Paris, 348 (2010), 379-383.
doi: 10.1016/j.crma.2010.02.003. |
[8] |
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), 507-522.
doi: 10.1088/0266-5611/23/2/004. |
[9] |
F. Cakoni and D. Gintides, New results on transmission eigenvalues, Inverse Problems and Imaging, 4 (2010), 39-48.
doi: 10.3934/ipi.2010.4.39. |
[10] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255.
doi: 10.1137/090769338. |
[11] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium, Applicable Analysis, 88 (2008), 475-493.
doi: 10.1080/00036810802713966. |
[12] |
F. Cakoni and A. Kirsch, On the interior transmission eigenvalue problem, Int. Jour. Comp. Sci. Math, 3 (2010), 142-167. |
[13] |
D. Colton and R. Kress, "Inverse Acoustic and Eletromagnetic Scattering Theory," Springer, New York, 2nd edition, 1998. |
[14] |
D. Colton, L. Päivärinta and J.Sylvester, The interior transmission problem, Inverse Problems and Imaging, 1 (2007), 13-28.
doi: 10.3934/ipi.2007.1.13. |
[15] |
A. Cossonniere and H. Haddar, The electromagnetic interior transmission problem for regions with cavities, SIAM J. Math. Anal., 43 (2011), 1698-1715.
doi: 10.1137/100813890. |
[16] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, Transmission eigenvalues for operators with constant coefficients, SIAM J. Math. Analysis, 42 (2010), 619-651.
doi: 10.1137/100793748. |
[17] |
M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, Transmission eigenvalues for operators with constant coefficients, Math Research Letters, 18 (2011), 279-293. |
[18] |
A. Kirsch, On the existence of transmission eigenvalues, Inverse Problems and Imaging, 3 (2009), 155-172. |
[19] |
A. Kirsch and N. Grinberg, The factorization method for inverse problems, in "Mathematics and its Applications," Oxford Lecture Series, 36, Oxford University Press, Oxford, 2008. |
[20] |
A. Kirsch and L. Päivärinta, On recovering obstacles inside inhomogeneities, Math. Meth. Appl. Sci., 21 (1998), 2965-2986.
doi: 10.1002/(SICI)1099-1476(19980510)21:7<619::AID-MMA940>3.0.CO;2-P. |
[21] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), 738-753.
doi: 10.1137/070697525. |
[22] |
J. Sylvester, Discreteness of transmission eigenvalues via upper triangular compact operators, SIAM J. Math. Anal., 44 (2012), 341-354.
doi: 10.1137/110836420. |
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