G. Allaire, Shape Optimization by the Homogenization Method, 2002.

A. Alvino, P. Lions, and G. Trombetti, Comparison results for elliptic and parabolic equations via symmetrization: a new approach, Differential Integral Equations, vol.4, issue.1, pp.25-50, 1991.

A. Alvino and G. Trombetti, A lower bound for the first eigenvalue of an elliptic operator, Journal of Mathematical Analysis and Applications, vol.94, issue.2, pp.328-337, 1983.

F. Belgacem, Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications. Chapman & Hall/CRC Research Notes in Mathematics Series, 1997.

F. Belgacem and C. Cosner, The effect of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Applied Mathematics Quarterly, vol.3, pp.379-397, 1995.

H. Berestycki, F. Hamel, and L. Roques, Analysis of the periodically fragmented environment model : I -species persistence, Journal of Mathematical Biology, vol.51, issue.1, pp.75-113, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00003742

H. Berestycki and T. Lachand-robert, Some properties of monotone rearrangement with applications to elliptic equations in cylinders, Math. Nachr, vol.266, pp.3-19, 2004.

P. Bernhard and A. Rapaport, On a theorem of danskin with an application to a theorem of von neumann-sion, Nonlinear Analysis: Theory, Methods & Applications, vol.24, pp.1163-1181, 1995.

B. Brandolini, F. Chiacchio, A. Henrot, and C. Trombetti, Existence of minimizers for eigenvalues of the dirichlet-laplacian with a drift, Journal of Differential Equations, vol.259, issue.2, pp.708-727, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01214040

A. Bressan, G. M. Coclite, and W. Shen, A multidimensional optimal-harvesting problem with measure-valued solutions, SIAM J. Control Optim, vol.51, issue.2, pp.1186-1202, 2013.

A. Bressan and W. Shen, Measure-valued solutions for a differential game related to fish harvesting, SIAM J. Control Optim, vol.47, issue.6, pp.3118-3137, 2008.

R. S. Cantrell and C. Cosner, Diffusive logistic equations with indefinite weights: Population models in disrupted environments II, SIAM Journal on Mathematical Analysis, vol.22, issue.4, pp.1043-1064, 1991.

J. Casado-díaz, Smoothness properties for the optimal mixture of two isotropic materials: The compliance and eigenvalue problems, SIAM J. Control and Optimization, vol.53, pp.2319-2349, 2015.

J. Casado-díaz, Some smoothness results for the optimal design of a two-composite material which minimizes the energy, Calculus of Variations and Partial Differential Equations, vol.53, issue.3, pp.649-673, 2015.

J. Casado-díaz, A characterization result for the existence of a two-phase material minimizing the first eigenvalue, vol.34, 2016.

F. Caubet, T. Deheuvels, and Y. Privat, Optimal location of resources for biased movement of species: the 1D case, SIAM Journal on Applied Mathematics, vol.77, issue.6, pp.1876-1903, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01514344

A. Cianchi, L. Esposito, N. Fusco, and C. Trombetti, A quantitative polya?szego principle, J. Reine Angew. Math

G. M. Coclite and M. Garavello, A time-dependent optimal harvesting problem with measure-valued solutions, SIAM J. Control Optim, vol.55, issue.2, pp.913-935, 2017.

C. Conca, A. Laurain, and R. Mahadevan, Minimization of the ground state for two phase conductors in low contrast regime, SIAM Journal of Applied Mathematics, vol.72, pp.1238-1259, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00625671

C. Conca, R. Mahadevan, and L. Sanz, An extremal eigenvalue problem for a two-phase conductor in a ball, Applied Mathematics and Optimization, vol.60, issue.2, pp.173-184, 2009.

C. Cosner and Y. Lou, Does movement toward better environments always benefit a population, Journal of Mathematical Analysis and Applications, vol.277, issue.2, pp.489-503, 2003.

S. Cox and R. Lipton, Extremal eigenvalue problems for two-phase conductors. Archive for Rational Mechanics and Analysis, vol.136, pp.101-117, 1996.

M. Dambrine and D. Kateb, On the shape sensitivity of the first dirichlet eigenvalue for two-phase problems, Applied Mathematics & Optimization, vol.63, issue.1, pp.45-74, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00868049

M. Dambrine and J. Lamboley, Stability in shape optimization with second variation, Journal of Differential Equations, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01073089

J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J. Lions, Homogenization and Effective Moduli of Materials and Media, 1986.

A. Ferone and R. Volpicelli, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.20, pp.333-339, 2003.

R. A. Fisher, The wave of advances of advantageous genes, Annals of Eugenics, vol.7, issue.4, pp.355-369, 1937.

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 1983.

F. Hamel, N. Nadirashvili, and E. Russ, Rearrangement inequalities and applications to isoperimetric problems for eigenvalues, Annals of Mathematics, vol.174, issue.2, pp.647-755, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00088786

G. H. Hardy, Note on a theorem of hilbert, Mathematische Zeitschrift, vol.6, issue.3, pp.314-317, 1920.

A. Henrot, Extremum Problems for Eigenvalues of Elliptic Operators, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00087731

A. Henrot, Shape Optimization and Spectral Theory, 2017.

A. Henrot and M. Pierre, Shape Variation and Optimization, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02094871

P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Communications in Partial Differential Equations, vol.5, issue.10, pp.999-1030, 1980.

C. Kao, Y. Lou, and E. Yanagida, Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains, Mathematical biosciences and engineering : MBE, vol.5, pp.315-350, 2008.

B. , Rearrangements and Convexity of Level Sets in PDE, 1985.

A. Kolmogoroff, I. Petrovsky, and N. Piscounoff, études de l'équation avec croissance de la quantité de matière et son applicationà un problème biologique, Moscow University Bulletin Of Mathematics, vol.1, p.1937

J. Lamboley, A. Laurain, G. Nadin, and Y. Privat, Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions, Calculus of Variations and Partial Differential Equations, vol.55, issue.6, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01295457

A. Laurain, Global minimizer of the ground state for two phase conductors in low contrast regime. ESAIM: Control, Optimisation and Calculus of Variations, vol.20, pp.362-388, 2014.

Y. Lou, Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics, pp.171-205, 2008.

Y. Lou and E. Yanagida, Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics, Japan Journal of Industrial and Applied Mathematics, vol.23, issue.3, p.275, 2006.

Y. Lou and E. Yanagida, Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics, Japan J. Indust. Appl. Math, vol.23, issue.3, pp.275-292, 2006.

I. Mazari, Quantitative inequality for the first eigenvalue of a schrödinger operator in the ball

N. G. Meyers, An l p -estimate for the gradient of solutions of second order elliptic divergence equations, Ser, vol.3, issue.3, pp.189-206, 1963.

F. Mignot, J. Puel, and F. Murat, Variation d'un point de retournement par rapport au domaine, Communications in Partial Differential Equations, vol.4, issue.11, pp.1263-1297, 1979.

F. Murat, Contre-exemples pour divers problèmes où le contrôle intervient dans les coefficients, vol.112, pp.49-68, 1977.

F. Murat and L. Tartar, Calculus of Variations and Homogenization, Birkhäuser Boston, pp.139-173, 1997.

J. D. Murray, Mathematical Biology, 1993.

G. Nadin, The effect of the schwarz rearrangement on the periodic principal eigenvalue of a nonsymmetric operator, SIAM Journal on Mathematical Analysis, vol.41, issue.6, pp.2388-2406, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01360636

O. Oleinik, A. Shamaev, and G. Yosifian, Mathematical Problems in Elasticity and Homogenization, Studies in Mathematics and its Applications), vol.26, 1992.

B. Opic and A. Kufner, Hardy-type Inequalities. Pitman research notes in mathematics series. Longman Scientific & Technical, 1990.

J. Serrin, A symmetry problem in potential theory, Archive for Rational Mechanics and Analysis, vol.43, issue.4, pp.304-318, 1971.

J. G. Skellam, Random dispersal in theoretical populations, Biometrika, vol.38, issue.1-2, p.1951