A. Bendali and K. Lemrabet, The Effect of a Thin Coating on the Scattering of a Time-Harmonic Wave for the Helmholtz Equation, SIAM Journal on Applied Mathematics, vol.56, issue.6, pp.1664-1693, 1996.
DOI : 10.1137/S0036139995281822

M. F. Betta, F. Brock, A. Mercaldo, and M. R. Posteraro, A weighted isoperimetric inequality and applications to symmetrization, Journal of Inequalities and Applications, vol.1999, issue.3, pp.215-240, 1999.
DOI : 10.1155/S1025583499000375

D. D. Bleecker, The spectrum of a Riemannian manifold with a unit Killing vector field, Transactions of the American Mathematical Society, vol.275, issue.1, pp.409-416, 1983.
DOI : 10.1090/S0002-9947-1983-0678360-0

V. Bonnaillie-noël, M. Dambrine, F. Hérau, and G. Vial, On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain, SIAM Journal on Mathematical Analysis, vol.42, issue.2, pp.931-945, 2010.
DOI : 10.1137/090756521

L. Brasco, G. De-philippis, and B. Ruffini, Spectral optimization for the Stekloff???Laplacian: The stability issue, Journal of Functional Analysis, vol.262, issue.11, pp.4675-4710, 2012.
DOI : 10.1016/j.jfa.2012.03.017
URL : https://hal.archives-ouvertes.fr/hal-00643643

F. Brock, An Isoperimetric Inequality for Eigenvalues of the Stekloff Problem, ZAMM, vol.3, issue.1, pp.69-71, 2001.
DOI : 10.1002/1521-4001(200101)81:1<69::AID-ZAMM69>3.0.CO;2-#

F. Caubet, M. Dambrine, and D. Kateb, Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions, Inverse Problems, vol.29, issue.11, pp.29-2013
DOI : 10.1088/0266-5611/29/11/115011
URL : https://hal.archives-ouvertes.fr/hal-00780735

F. H. Clarke, Optimization and nonsmooth analysis Series of Monographs and Advanced Texts, 1983.

B. Colbois and J. Dodziuk, Riemannian Metrics with Large ?? 1, Proc. Amer, pp.905-906, 1994.
DOI : 10.2307/2160770

B. Colbois, E. B. Dryden, and A. Soufi, Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds, Bulletin of the London Mathematical Society, vol.42, issue.1, pp.96-108, 2010.
DOI : 10.1112/blms/bdp100
URL : https://hal.archives-ouvertes.fr/hal-00420689

M. Dambrine and D. Kateb, Persistency of wellposedness of Ventcel???s boundary value problem under shape deformations, Journal of Mathematical Analysis and Applications, vol.394, issue.1, pp.129-138, 2012.
DOI : 10.1016/j.jmaa.2012.04.018

M. C. Delfour and J. Zolésio, Shapes and geometries, volume 4 of Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM) Analysis, 2001.

F. R. Desaint and J. Zolésio, Manifold Derivative in the Laplace???Beltrami Equation, Journal of Functional Analysis, vol.151, issue.1, pp.234-269, 1997.
DOI : 10.1006/jfan.1997.3130

G. R. Goldstein, Derivation and physical interpretation of general boundary conditions, Adv. Differential Equations, vol.11, issue.4, pp.457-480, 2006.

H. Haddar, P. Joly, and H. Nguyen, GENERALIZED IMPEDANCE BOUNDARY CONDITIONS FOR SCATTERING BY STRONGLY ABSORBING OBSTACLES: THE SCALAR CASE, Mathematical Models and Methods in Applied Sciences, vol.15, issue.08, pp.1273-1300, 2005.
DOI : 10.1142/S021820250500073X
URL : https://hal.archives-ouvertes.fr/hal-00743895

A. Henrot and M. Pierre, Variation et optimisation de formes, ) [Mathematics & Applications, 2005.
DOI : 10.1007/3-540-37689-5

]. J. Hersch, Caractérisation variationnelle d'une somme de valeurs propres consécutives

J. Hersch, Quatre propriétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris Sér. A-B, vol.270, pp.1645-1648, 1970.

G. N. Hile and Z. Y. Xu, Inequalities for Sums of Reciprocals of Eigenvalues, Journal of Mathematical Analysis and Applications, vol.180, issue.2, pp.412-430, 1993.
DOI : 10.1006/jmaa.1993.1409

J. Kennedy, A Faber-Krahn inequality for the Laplacian with Generalised Wentzell boundary conditions, Journal of Evolution Equations, vol.8, issue.3, pp.557-582, 2008.
DOI : 10.1007/s00028-008-0393-4

K. Lemrabet and D. Teniou, Vibrations d'une plaque mince avec raidisseur sur le bord, Maghreb Math. Rev, vol.2, issue.1, pp.27-41, 1992.

J. Nédélec, Acoustic and electromagnetic equations Integral representations for harmonic problems, Applied Mathematical Sciences, vol.144, 2001.

J. H. Ortega and E. Zuazua, Generic simplicity of the eigenvalues of the Stokes system in two space dimensions, Adv. Differential Equations, vol.6, issue.8, pp.987-1023, 2001.

E. M. Stein, G. Weiss, and N. J. , Introduction to Fourier analysis on Euclidean spaces, 1971.