G. Alberti, Variational models for phase transitions, an approach via gamma-convergence, 1998.

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs, 2000.

P. R. Antunes and P. Freitas, Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians, J. Optim. Theory Appl, vol.154, issue.1, pp.235-257, 2012.

P. R. Antunes and P. Freitas, Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction, 2014.

A. H. Barnett and T. Betcke, Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains, J. Comput. Phys, vol.227, issue.14, pp.7003-7026, 2008.

C. A. Berenstein, An inverse spectral theorem and its relation to the Pompeiu problem, J. Analyse Math, vol.37, pp.128-144, 1980.

A. Berger, The eigenvalues of the Laplacian with Dirichlet boundary condition in R 2 are almost never minimized by disks, Ann. Global Anal. Geom, vol.47, issue.3, pp.285-304, 2015.

B. Bourdin, D. Bucur, and . Oudet, Optimal partitions for eigenvalues, SIAM J. Sci. Comput, vol.31, issue.6, pp.4100-4114, 2009.

A. Braides, Approximation of Free-Discontinuity Problems, 1998.

A. Braides, Gamma-Convergence for beginners, 2002.

D. Bucur and G. Buttazzo, Variational methods in shape optimization problems, Progress in Nonlinear Differential Equations and their Applications, vol.65, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00414080

D. Bucur, G. Buttazzo, and A. Henrot, Minimization of ?2(?) with a perimeter constraint, Indiana Univ. Math. J, vol.58, issue.6, pp.2709-2728, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00201946

G. Buttazzo, Gamma-convergence and its Applications to Some Problems in the Calculus of Variations. School on Homogenization ICTP, 1993.

G. Maso and F. Murat, Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.24, issue.4, pp.239-290, 1997.

G. De-philippis and B. Velichkov, Existence and regularity of minimizers for some spectral functionals with perimeter constraint, Appl. Math. Optim, vol.69, issue.2, pp.199-231, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02014018

A. E. Soufi and S. Ilias, Riemannian manifolds admitting isometric immersions by their first eigenfunctions, Pacific J. Math, vol.195, issue.1, pp.91-99, 2000.

A. E. Soufi and S. Ilias, Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold, Illinois J. Math, vol.51, issue.2, pp.645-666, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00145250

A. Henrot, Extremum problems for eigenvalues of elliptic operators, Frontiers in Mathematics, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00087731

A. Henrot and M. Pierre, Variation et optimisation de formes, Mathématiques & Applications, vol.48

. Springer, Une analyse géométrique, 2005.

L. Modica and S. Mortola, Un esempio di ? ?-convergenza, Boll. Un. Mat. Ital. B, vol.14, issue.5, pp.285-299, 1977.

N. Nadirashvili, Berger's isoperimetric problem and minimal immersions of surfaces, Geom. Funct. Anal, vol.6, issue.5, pp.877-897, 1996.

A. A. Novotny and J. Soko, Topological derivatives in shape optimization, Interaction of Mechanics and Mathematics, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01304757

B. Osting, Optimization of spectral functions of Dirichlet-Laplacian eigenvalues, J. Comput. Phys, vol.229, issue.22, pp.8578-8590, 2010.

B. Osting and C. Kao, Minimal convex combinations of three sequential Laplace-Dirichlet eigenvalues, Appl. Math. Optim, vol.69, issue.1, pp.123-139, 2014.

´. E. Oudet, Numerical minimization of eigenmodes of a membrane with respect to the domain, ESAIM Control Optim. Calc. Var, vol.10, issue.3, pp.315-330, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00384996

E. Oudet, Approximation of partitions of least perimeter by ?-convergence: around Kelvin's conjecture, Exp. Math, vol.20, issue.3, pp.260-270, 2011.

M. Schmidt and . Minfunc, , 2012.

L. Stewart, Matlab lbfgs wrapper

S. A. Williams, Boundary regularity for a family of overdetermined problems for the Helmholtz equation, J. Math. Anal. Appl, vol.274, issue.1, pp.296-304, 2002.