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Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
The perturbation of transmission eigenvalues for inhomogeneous media in the presence of small penetrable inclusions
1. | Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, United States |
2. | Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, United States, United States |
References:
[1] |
S. Agmon, Lectures on Elliptic Boundary Value Problems,, Van Nostrand-Reinhold, (1965).
|
[2] |
C. Amrouche and M. Fontes, Biharmonic problem in exterior domains of $\mathbbR^n$: An approach with weighted Sobolev spaces,, J. Math. Anal. Appl., 304 (2005), 552.
doi: 10.1016/j.jmaa.2004.09.039. |
[3] |
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.
doi: 10.1016/j.crma.2010.02.003. |
[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), 507.
doi: 10.1088/0266-5611/23/2/004. |
[5] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues,, SIAM J. Math. Anal., 42 (2010), 237.
doi: 10.1137/090769338. |
[6] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium,, Appl. Anal., 88 (2009), 475.
doi: 10.1080/00036810802713966. |
[7] |
_________, Transmission eigenvalues in inverse scattering theory,, in Inverse Problems and Applications: Inside Out. II, (2013), 529.
|
[8] |
F. Cakoni and S. Moskow, Asymptotic expansions for transmission eigenvalues for media with small inhomogeneities,, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/10/104014. |
[9] |
D. Colton, L. Päivärinta and J. Sylvester, The interior transmission problem,, Inverse Problems and Imaging, 1 (2007), 13.
doi: 10.3934/ipi.2007.1.13. |
[10] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, reprint of 1998 edition, (1998).
|
[11] |
G. Giorgi and H. Haddar, Computing estimates of material properties from transmission eigenvalues,, Inverse Problems, 28 (2012).
doi: 10.1088/0266-5611/28/5/055009. |
[12] |
I. Godberg and P. Lancaster, Indefinite Linear Algebra and Applications,, L. Rodman, (2005).
|
[13] |
A. Kirsch and A. Lechleiter, The inside-outside duality for scattering problems by inhomogeneous media,, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/10/104011. |
[14] |
S. Moskow, Nonlinear eigenvalue approximation for compact operators,, preprint, (2014). Google Scholar |
[15] |
J. E. Osborn, Spectral approximation for compact operators,, Math. Comput., 29 (1975), 712.
doi: 10.1090/S0025-5718-1975-0383117-3. |
[16] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues,, SIAM J. Math. Anal, 40 (2008), 738.
doi: 10.1137/070697525. |
[17] |
L. Robbiano, Spectral analysis of the interior transmission eigenvalue problem,, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/10/104001. |
show all references
References:
[1] |
S. Agmon, Lectures on Elliptic Boundary Value Problems,, Van Nostrand-Reinhold, (1965).
|
[2] |
C. Amrouche and M. Fontes, Biharmonic problem in exterior domains of $\mathbbR^n$: An approach with weighted Sobolev spaces,, J. Math. Anal. Appl., 304 (2005), 552.
doi: 10.1016/j.jmaa.2004.09.039. |
[3] |
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.
doi: 10.1016/j.crma.2010.02.003. |
[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), 507.
doi: 10.1088/0266-5611/23/2/004. |
[5] |
F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues,, SIAM J. Math. Anal., 42 (2010), 237.
doi: 10.1137/090769338. |
[6] |
F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogeneous medium,, Appl. Anal., 88 (2009), 475.
doi: 10.1080/00036810802713966. |
[7] |
_________, Transmission eigenvalues in inverse scattering theory,, in Inverse Problems and Applications: Inside Out. II, (2013), 529.
|
[8] |
F. Cakoni and S. Moskow, Asymptotic expansions for transmission eigenvalues for media with small inhomogeneities,, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/10/104014. |
[9] |
D. Colton, L. Päivärinta and J. Sylvester, The interior transmission problem,, Inverse Problems and Imaging, 1 (2007), 13.
doi: 10.3934/ipi.2007.1.13. |
[10] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, reprint of 1998 edition, (1998).
|
[11] |
G. Giorgi and H. Haddar, Computing estimates of material properties from transmission eigenvalues,, Inverse Problems, 28 (2012).
doi: 10.1088/0266-5611/28/5/055009. |
[12] |
I. Godberg and P. Lancaster, Indefinite Linear Algebra and Applications,, L. Rodman, (2005).
|
[13] |
A. Kirsch and A. Lechleiter, The inside-outside duality for scattering problems by inhomogeneous media,, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/10/104011. |
[14] |
S. Moskow, Nonlinear eigenvalue approximation for compact operators,, preprint, (2014). Google Scholar |
[15] |
J. E. Osborn, Spectral approximation for compact operators,, Math. Comput., 29 (1975), 712.
doi: 10.1090/S0025-5718-1975-0383117-3. |
[16] |
L. Päivärinta and J. Sylvester, Transmission eigenvalues,, SIAM J. Math. Anal, 40 (2008), 738.
doi: 10.1137/070697525. |
[17] |
L. Robbiano, Spectral analysis of the interior transmission eigenvalue problem,, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/10/104001. |
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