The interior transmission eigenvalue problem

SIAM Journal on Mathematical Analysis

Volumn 42, Issue 6, 2010, Pages 2912-2921

  Cakoni, Fioralba ^a   Colton, David ^a   Gintides, Drossos ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Inhomogeneous medium; Interior transmission problem; Inverse scattering; Transmission eigenvalues

Indexed keywords

COMPLEX EIGENVALUES; COMPLEX PLANES; EIGEN-VALUE; EIGENVALUE PROBLEM; EIGENVALUES; FIELD PATTERNS; HOMOGENEOUS MEDIA; INDEX OF REFRACTION; INHOMOGENEOUS MEDIUM; INTERIOR TRANSMISSION PROBLEMS; INVERSE SCATTERING; SCATTERED WAVES;

INVERSE PROBLEMS; REFRACTION; REFRACTIVE INDEX; SCATTERING;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 78649801117     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/100793542     Document Type: Article

References (15)

1. F. CAKONI, D. COLTON, AND H. HADDAR, The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data, J. Integral Equations Appl., 21 (2009), pp. 203-227.
2. F. CAKONI, D. COLTON, AND H. HADDAR, On the determination of Dirichlet or transmission eigenvalues from far field data, C. R. Math. Acad. Sci. Paris, Ser. I, 348 (2010) pp. 379-383.
3. F. CAKONI AND D. GINTIDES, New results on transmission eigenvalues, Inverse Prob. Imaging, 1 (2007), pp. 13-28.
4. 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.
5. D. COLTON, Analytic Theory of Partial Differential Equations, Pitman, Boston, 1980.
6. D. COLTON AND R. KRESS, The construction of solutions to acoustic scattering problems in a spherically stratified medium II, Quart. J. Mech. Appl. Math., 32 (1972), pp. 53-62.
7. D. COLTON AND R. KRESS, Integral Equation Methods in Scattering Theory, John Wiley, New York, 1983.
8. D. COLTON AND R. KRESS, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Springer, New York, 1998.
9. D. COLTON, L. P̈IV̈RINTA, AND J. SYLVESTER, The interior transmission problem, Inverse Prob. Imaging, 1 (2007), pp. 13-28.
10. P.J. DAVIS, Interpolation and Approximation, Dover, New York, 1975.
11. A. KIRSCH, On the existence of transmission eigenvalues, Inverse Prob. Imaging, 3 (2009), pp. 155-172.
12. J. MCLAUGHLIN AND P. POLYAKOV, On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues, J. Differential Equations, 107 (1994), pp. 351-382.
13. J. MCLAUGHLIN, P. POLYAKOV, AND P. SACKS, Reconstruction of a spherically symmetric speed of sound, SIAM J. Appl. Math., 54 (1994), pp. 1203-1223.
14. L. P̈IV̈RINTA AND J. SYLVESTER, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), pp. 738-753.
15. E. STEIN AND R. SKAKARCHI, Complex Analysis, Princeton University Press, Princeton, NJ, 2003.