Strongly oscillating singularities for the interior transmission eigenvalue problem

Inverse Problems

Volumn 29, Issue 10, 2013, Pages

  Dhia, Anne Sophie Bonnet Ben ^a   Chesnel, Lucas ^b  

^a Centre National de la Recherche Scientifique   (France)

^b AALTO UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE SETS; FREDHOLM; FREDHOLMNESS; SIGN-ON; TRANSMISSION EIGENVALUE; TRANSMISSION EIGENVALUES; VARIATIONAL APPROACHES;

COMPOSITE MATERIALS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84884645336     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/29/10/104004     Document Type: Article

References (33)

1. Bonnet-Ben Dhia A-S, Chesnel L and Ciarlet P Jr 2012 T-coercivity for scalar interface problems between dielectrics and metamaterials Math. Modelling Numer. Anal. 46 1363-87
2. Bonnet-Ben Dhia A-S, Chesnel L and Claeys X 2013 Radiation condition for a non-smooth interface between a dielectric and a metamaterial Math. Models Methods Appl. Sci. 23 1629-62
3. Bonnet-Ben Dhia A-S, Chesnel L and Haddar H 2011 On the use of T-coercivity to study the interior transmission eigenvalue problem C. R. Acad. Sci., Paris I 340 647-51
4. Bonnet-Ben Dhia A-S, Ciarlet P Jr and Zwölf C M 2010 Time harmonic wave diffraction problems in materials with sign-shifting coefficients J. Comput. Appl. Math. 234 1912-9
5. Bonnet-Ben Dhia A-S, Ciarlet P Jr and Zwölf C M 2010 Corrigendum: Time harmonic wave diffraction problems in materials with sign-shifting coefficients J. Comput. Appl. Math. 234 2616
6. Bonnet-Ben Dhia A-S, Dauge M and Ramdani K 1999 Analyse spectrale et singularités d'un problème de transmission non coercif C. R. Acad. Sci., Paris I 328 717-20
7. Cakoni F, Colton D and Haddar H 2002 The linear sampling method for anisotropic media J. Comput. Appl. Math. 146 285-99
8. Cakoni F, Colton D and Haddar H 2009 The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data J. Integr. Eqns Appl. 21 203-27
9. Cakoni F and Haddar H 2007 A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media Inverse Problems Imaging 1 443-56
10. Cakoni F and Kirsch A 2010 On the interior transmission eigenvalue problem Int. J. Comput. Sci. Math. 3 142-67
11. Chesnel L 2012 Interior transmission eigenvalue problem for Maxwell's equations: the T-coercivity as an alternative approach Inverse Problems 28 065005
12. Chesnel L 2012 Investigation of some transmission problems with sign-changing coefficients. Application to metamaterials PhD Thesis cole Polytechnique
13. Chesnel L and Ciarlet P Jr 2011 Compact imbeddings in electromagnetism with interfaces between classical materials and metamaterials SIAM J. Math. Anal. 43 2150-69
14. Colton D and Monk P 1988 The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium Q. J. Mech. Appl. Math. 41 97-125
15. Colton D and Païvärinta L 2000 Transmission eigenvalues and a problem of Hans Lewy J. Comput. Appl. Math. 117 91-104
16. Colton D, Païvärinta L and Sylvester J 2007 The interior transmission problem Inverse Problems Imaging 1 13
17. Costabel M and Stephan E 1985 A direct boundary integral method for transmission problems J. Math. Anal. Appl. 106 367-413 (Pubitemid 15545555)
18. Dauge M and Texier B 1997 Problèmes de transmission non coercifs dans des polygones Technical Report 97-27 Université de Rennes 1, IRMAR, Rennes Cedex, France (http://hal.archives-ouvertes.fr/docs/00/56/23/29/PDF/ BenjaminT-arxiv.pdf)
19. Haddar H 2004 The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem Math. Methods Appl. Sci. 27 2111-29
20. Kondratiev V A 1967 Boundary-value problems for elliptic equations in domains with conical or angular points Trans. Moscow Math. Soc. 16 227-313
21. Kozlov V A, Maz'ya V G and Rossmann J 1997 Elliptic Boundary Value Problems in Domains with Point Singularities (Mathematical Surveys and Monographs vol 52) (Providence, RI: American Mathematical Society)
22. Lakshtanov E and Vainberg B 2012 Ellipticity in the interior transmission problem in anisotropic media SIAM J. Math. Anal. 44 1165-74
23. Lions J-L and Magenes E 1968 Problèmes aux Limites Non Homogènes et Applications (Paris: Dunod)
24. Mazya V, Nazarov S A and Plamenevskiǐ B 2000 Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains vols 1, 2 (Basel: Birkhäuser)
25. McLean W 2000 Strongly Elliptic Systems and Boundary Integral Equations (Cambridge: Cambridge University Press)
26. Nazarov S A and Plamenevskiǐ B A 1990 Radiation conditions for selfadjoint elliptic problems Dokl. Akad. Nauk SSSR 311 532-6
27. Nazarov S A and Plamenevskiǐ B A 1994 Elliptic Problems in Domains With Piecewise Smooth Boundaries (Expositions in Mathematics vol 13) (Berlin: de Gruyter)
28. Nazarov S A and Taskinen J 2011 Radiation conditions at the top of a rotational cusp in the theory of water-waves Math. Modelling Numer. Anal. 45 947-79
29. Ola P 1995 Remarks on a transmission problem J. Math. Anal. Appl. 196 639-58
30. Peetre J 1961 Another approach to elliptic boundary problems Commun. Pure Appl. Math. 14 711-31
31. Roǐtberg J A and Šeftel′ Z G 1963 General boundary-value problems for elliptic equations with discontinuous coefficients Dokl. Akad. Nauk SSSR 148 1034-7
32. Rynne B P and Sleeman B D 1991 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755-62
33. Schechter M 1960 A generalization of the problem of transmission Ann. Scuola Norm. Super. Pisa 14 207-36