]. A. Références1, M. Abdulle, S. Huber, and . Lemaire, An optimization-based numerical method for diffusion problems with sign-changing coefficients, p.1354092, 2016.

I. Babu?ka and J. Osborn, Eigenvalue problems, Handbook of numerical analysis, P.G. Ciarlet and J.-L. Lions Editors, vol.II, pp.641-787, 1991.

A. Bonnet-ben-dhia, L. Chesnel, and P. Ciarlet-jr, -coercivity for scalar interface problems between dielectrics and metamaterials, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.6, pp.1363-1387, 2012.
DOI : 10.1051/m2an/2012006
URL : https://hal.archives-ouvertes.fr/hal-00717640

A. Bonnet-ben-dhia, C. Carvalho, and P. Ciarlet-jr, Mesh requirements for the finite element approximation of problems with sign-changing coefficients, pp.1335153-1335154, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01335153

A. Bonnet-ben-dhia, P. Ciarlet-jr, and C. M. Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients, Journal of Computational and Applied Mathematics, vol.234, issue.6, pp.1912-1919, 2010.
DOI : 10.1016/j.cam.2009.08.041
URL : https://hal.archives-ouvertes.fr/hal-00975073

L. Chesnel and P. Ciarlet-jr, Compact Imbeddings in Electromagnetism with Interfaces between Classical Materials and Metamaterials, SIAM Journal on Mathematical Analysis, vol.43, issue.5, pp.2150-2169, 2011.
DOI : 10.1137/100810903
URL : https://hal.archives-ouvertes.fr/hal-00602904

L. Chesnel and P. Ciarlet-jr, T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients, Numerische Mathematik, vol.54, issue.190, pp.1-29, 2013.
DOI : 10.1007/s00211-012-0510-8
URL : https://hal.archives-ouvertes.fr/hal-00688862

M. Delfour and J. Zolésio, Shapes and geometries : metrics, analysis, differential calculus and optimization, 2011.
DOI : 10.1137/1.9780898719826

J. Fleckinger and M. L. Lapidus, Eigenvalues of elliptic boundary value problems with an indefinite weight function, Transactions of the American Mathematical Society, vol.295, issue.1, pp.305-324, 1986.
DOI : 10.1090/S0002-9947-1986-0831201-3

S. Nicaise and J. Venel, A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients, Journal of Computational and Applied Mathematics, vol.235, issue.14, pp.4272-4282, 2011.
DOI : 10.1016/j.cam.2011.03.028
URL : https://hal.archives-ouvertes.fr/hal-00517989

E. Séré and M. Lewin, Spectral pollution and how to avoid it (with applications to Dirac and periodic Schrödinger operators, Proc. London Math. Soc, pp.864-900, 2010.