M. Abramowitz and I. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 1965.

R. A. Adams and J. F. Fournier, Sobolev spaces, 2003.

G. Allaire, Shape optimization by the homogenization method, 2001.

G. Allaire, Conception optimale de structures, Mathématiques & Applications, vol.58, 2006.

G. Allaire, E. Bonnetier, G. Francfort, and F. Jouve, Shape optimization by the homogenization method, Numerische Mathematik, vol.76, issue.1, pp.27-68, 1997.
DOI : 10.1007/s002110050253

G. Allaire, C. Dapogny, G. Delgado, and G. Michailidis, Multi-phase optimization via a level set method, ESAIM: Control, Optimization and Calculus of Variations, pp.576-611, 2014.

G. Allaire, F. Jouve, and N. Van-goethem, Damage and fracture evolution in brittle materials by shape optimization methods, Journal of Computational Physics, vol.230, issue.12, pp.5010-5044, 2011.
DOI : 10.1016/j.jcp.2011.03.024

URL : https://hal.archives-ouvertes.fr/hal-00784048

L. Ambrosio and G. Buttazzo, An optimal design problem with perimeter penalization, Calculus of Variations and Partial Differential Equations, pp.1-55, 1993.

H. Ammari and H. Kang, Polarization and Moment Tensors; With Applications to Inverse Problems and Effective Medium Theory, p.162, 2007.

S. Amstutz, Sensitivity analysis with respect to a local perturbation of the material property, Asympt. Anal, vol.49, pp.87-108, 2006.

S. Amstutz, Analysis of a level set method for topology optimization, Optimization Methods and Software, pp.555-573, 2011.

S. Amstutz, Connections between topological sensitivity analysis and material interpolation schemes in topology optimization, Structural and Multidisciplinary Optimization, vol.37, issue.4, pp.755-765, 2011.
DOI : 10.1137/S0363012997323230

URL : https://hal.archives-ouvertes.fr/hal-01325799

S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, vol.216, issue.2, pp.573-588, 2006.
DOI : 10.1016/j.jcp.2005.12.015

M. Beckers, Topology optimization using a dual method with discrete variables, Structural Optimization, pp.14-24, 1999.

M. P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988.
DOI : 10.1016/0045-7825(88)90086-2

M. Bendsøe and O. Sigmund, Material interpolation schemes in topology optimization, Archive of Applied Mechanics, pp.635-654, 1999.

M. Bendsøe and O. Sigmund, Topology Optimization. Theory, Methods, and Applications, 2003.

A. Bensoussan, J. Lions, and G. Papanicolau, Asymptotic analysis of periodic structures, 1978.

M. Bonnet and G. Delgado, The topological derivative in anisotropic elasticity, The Quarterly Journal of Mechanics and Applied Mathematics, vol.66, issue.4, pp.557-586, 2013.
DOI : 10.1093/qjmam/hbt018

URL : https://hal.archives-ouvertes.fr/hal-00852248

T. Borrvall and J. Petersson, Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids, vol.24, issue.1, pp.41-77, 2003.
DOI : 10.1007/978-3-662-12613-4

B. Bourdin, Filters in topology optimization, International Journal for Numerical Methods in Engineering, vol.18, issue.9, pp.2143-2158, 2001.
DOI : 10.1007/BF01210686

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2000.
DOI : 10.1007/978-0-387-70914-7

T. E. Bruns and D. A. Tortorelli, Topology optimization of non-linear elastic structures and compliant mechanisms, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.26-27, pp.3443-3459, 2001.
DOI : 10.1016/S0045-7825(00)00278-4

D. Bucur and G. Buttazzo, Variational Methods in Shape Optimization Problems, Birkäuser, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00414080

J. Céa, Conception optimale ou identification de formes, calcul rapide de la d??riv??e directionnelle de la fonction co??t, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, issue.3, pp.371-420, 1986.
DOI : 10.1051/m2an/1986200303711

J. Céa, S. Garreau, P. Guillaume, and M. Masmoudi, The shape and topological optimizations connection, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.4, pp.713-726, 2000.
DOI : 10.1016/S0045-7825(99)00357-6

C. Dapogny, Shape optimization, level set methods on unstructured meshes and mesh evolution, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00916224

M. C. Delfour and J. Zolesio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2011.
DOI : 10.1137/1.9780898719826

A. Ern and J. Guermond, Theory and Practice of Finite Elements, 2004.
DOI : 10.1007/978-1-4757-4355-5

A. Evgrafov, Topology optimization of slightly compressible fluids, ZAMM, vol.40, issue.3, pp.46-62, 2006.
DOI : 10.1080/08905459708945415

S. M. Giusti, A. Ferrer, and J. Oliver, Topological sensitivity analysis in heterogeneous anisotropic elasticity problem. Theoretical and computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.311, pp.311-134, 2016.
DOI : 10.1016/j.cma.2016.08.004

R. B. Haber, C. S. Jog, and M. P. Bendsöe, A new approach to variable-topology shape design using a constraint on perimeter, Structural Optimization, pp.1-12, 1996.

A. Henrot and M. Pierre, Variation et optimisation de formes, une analyse géométrique, Mathématiques et Applications, vol.48, 2005.
DOI : 10.1007/3-540-37689-5

K. Ito, K. Kunisch, and G. Peichl, Variational approach to shape derivatives, ESAIM: Control, Optimisation and Calculus of Variations, vol.14, issue.3, pp.517-539, 2008.
DOI : 10.1051/cocv:2008002

URL : http://www.esaim-cocv.org/articles/cocv/pdf/2008/03/cocv0641.pdf

P. K. Kythe, Fundamental Solutions for partial differential operators, and applications, 1996.

B. S. Lazarov and O. Sigmund, Filters in topology optimization based on Helmholtz-type differential equations, International Journal for Numerical Methods in Engineering, vol.79, issue.11, pp.765-781, 2011.
DOI : 10.1002/nme.2579

F. Murat and J. Simon, Sur le contrôle par un domaine géométrique, 1976.

F. Murat and L. Tartar, Calculus of Variations and Homogenization, in Topics in the mathematical modelling of composite materials, Progr. NonLinear Differential Equations, pp.139-173, 1997.

L. Nirenberg, Remarks on strongly elliptic partial differential equations, Communications on Pure and Applied Mathematics, vol.7, issue.4, pp.649-675, 1955.
DOI : 10.7146/math.scand.a-10364

A. Novotny and J. Sokolowski, Topological derivatives in shape optimization, 2012.
DOI : 10.1007/978-3-642-35245-4

URL : https://hal.archives-ouvertes.fr/hal-01304757

S. Osher and J. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

O. Pantz, Sensibilit?? de l'??quation de la chaleur aux sauts de conductivit??, Comptes Rendus Mathematique, vol.341, issue.5, pp.333-337, 2005.
DOI : 10.1016/j.crma.2005.07.005

J. Petersson, Some convergence results in perimeter-controlled topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.171, issue.1-2, pp.123-140, 1999.
DOI : 10.1016/S0045-7825(98)00248-5

J. Petersson and O. Sigmund, Slope constrained topology optimization, International Journal for Numerical Methods in Engineering, vol.89, issue.8, pp.41-1417, 1998.
DOI : 10.1016/0045-7825(91)90044-7

A. Quarteroni, Numerical Models for Differential Problems, 2014.

J. Sethian, Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 1999.

O. Sigmund, On the design of compliant mechanisms using topology optimization, Mechanical Structures and Machines, pp.493-524, 1997.

O. Sigmund and J. Petersson, Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Structural Optimization, vol.89, issue.1, pp.68-75, 1998.
DOI : 10.1007/BF01214002

J. Sokolowski and J. Zolesio, Introduction to Shape Optimization; Shape Sensitivity Analysis, 1992.

N. Suzuki and N. Kikuchi, A homogenization method for shape and topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.93, issue.3, pp.291-318, 1991.
DOI : 10.1016/0045-7825(91)90245-2