G. Allaire, Conception optimale de structures, 2006.

F. Bobaru and S. Rachakonda, Optimal shape profiles for cooling fins of high and low conductivity, International Journal of Heat and Mass Transfer, vol.47, issue.23, pp.4953-4966, 2004.
DOI : 10.1016/j.ijheatmasstransfer.2004.06.013

B. P. Belinskiy, J. W. Hiestand, and M. L. Mccarthy, Optimal design of a bar with an attached mass for maximizing the heat transfer, Electron. J. Differential Equations, issue.181, p.13, 2012.

J. F. Bonnans, J. Ch, C. Gilbert, and C. Lemar-`-echallemar-`-lemar-`-echal, Sagastiz·bal Numerical Optimization: Theoretical and Practical Aspects, 2003.

Y. M. Chang, J. W. Cleaver, and C. K. Chen, Transient Response of Fins by Optimal Linearization and Variational Embedding Methods, Journal of Heat Transfer, vol.104, issue.4, pp.813-815, 1982.
DOI : 10.1115/1.3245211

C. H. Chiu and C. K. Chen, A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, International Journal of Heat and Mass Transfer, vol.45, issue.10, pp.2067-2075, 2002.
DOI : 10.1016/S0017-9310(01)00286-1

S. J. Cox and R. Lipton, Extremal eigenvalue problems for two-phase conductors, Archive for Rational Mechanics and Analysis, vol.447, issue.1, pp.101-117, 1996.
DOI : 10.1007/BF02316974

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A modeling language for mathematical programming, 2002.

G. L. Grodzovskii and Z. V. Pasechnik, Optimum shape of radiation-cooled ring fins, Journal of Applied Mechanics and Technical Physics, vol.2, issue.3, pp.102-105, 1967.
DOI : 10.1007/BF00913229

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

A. Henrot and Y. Privat, Shape Minimization of Dendritic Attenuation, Applied Mathematics and Optimization, vol.133, issue.10, pp.1-16, 2008.
DOI : 10.1007/s00245-007-9002-0
URL : https://hal.archives-ouvertes.fr/hal-00128444

A. Henrot and M. Pierre, Variation et optimisation de formes, Mathématiques et applications, 2005.
DOI : 10.1007/3-540-37689-5

M. Horváth, On the first two eigenvalues of Sturm-Liouville operators, Proc. Amer. Math. Soc. 131, pp.1215-1224, 2003.

M. Huang, A note on the eigenvalue ratio of vibrating strings, Proc. Amer, pp.1805-1813, 1999.
DOI : 10.1007/s10474-009-8107-0

C. Huang and C. Wuchiu, A shape design problem in determining the interfacial surface of two bodies based on the desired system heat flux, International Journal of Heat and Mass Transfer, vol.54, issue.11-12, pp.11-12, 2011.
DOI : 10.1016/j.ijheatmasstransfer.2011.02.010

M. G. Krein, On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability, Amer, Math. Soc. Transl, issue.2 1, pp.163-187, 1955.

S. P. Liaw and R. H. Yeh, Fins with temperature dependent surface heat flux???I. Single heat transfer mode, International Journal of Heat and Mass Transfer, vol.37, issue.10, pp.1509-1515, 1994.
DOI : 10.1016/0017-9310(94)90152-X

T. J. Mahar and B. E. Willner, An extremal eigenvalue problem, Communications on Pure and Applied Mathematics, vol.29, issue.5, pp.517-529, 1976.
DOI : 10.1002/cpa.3160290505

T. J. Mahar and B. E. Willner, Extrema of functions of eigenvalues, J. Math. Anal. Appl, vol.72, issue.2, pp.730-739, 1979.

G. Marck, M. Nemer, and J. Harion, Topology Optimization of Heat and Mass Transfer Problems: Laminar Flow, Numerical Heat Transfer, Part B: Fundamentals, vol.45, issue.6, pp.508-539, 2013.
DOI : 10.1137/S1052623499362822
URL : https://hal.archives-ouvertes.fr/hal-00880111

L. Marin, L. Elliott, P. J. Heggs, D. B. Ingham, D. Lesnic et al., Analysis of polygonal fins using the boundary element method, Applied Thermal Engineering, vol.24, issue.8-9, pp.1321-1339, 2004.
DOI : 10.1016/j.applthermaleng.2003.12.022

Y. Privat, The optimal shape of a dendrite sealed at both ends, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.6, pp.2317-2333, 2009.
DOI : 10.1016/j.anihpc.2009.04.004
URL : https://hal.archives-ouvertes.fr/hal-00359472

A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, vol.10, issue.1, pp.25-57, 2006.
DOI : 10.1007/s10107-004-0559-y