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Issue ESAIM: COCV
Volume 10, Number 3, July 2004
Page(s) 315 - 330
DOI 10.1051/cocv:2004011

References of  July 2004, Vol. 10, 315-330
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  3. M. Bendsoe, Optimization of structural Topology, Shape and Material. Springer (1995).
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  5. G. Buttazzo and G. Dal Maso, An Existence Result for a Class of Shape Optimization Problems. Arch. Ration. Mech. Anal. 122 (1993) 183-195.
  6. M.G. Crandall and P.L. Lions, Viscosity Solutions of Hamilton-Jacobi Equations. Trans. Amer. Math. Soc. 277 (1983) 1-43 [MathSciNet].
  7. G. Faber, Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt. Sitz. Ber. Bayer. Akad. Wiss. (1923) 169-172.
  8. S. Finzi Vita, Constrained shape optimization for Dirichlets problems: discretization via relaxation. Adv. Math. Sci. Appl. 9 (1999) 581-596.
  9. H. Hamda, F. Jouve, E. Lutton, M. Schoenauer and M. Sebag, Représentations non structurées en optimisation topologique de formes par algorithmes évolutionnaires. Actes du 32$^{\rm e}$ Congrès d'Analyse Numérique, Canum. ESAIM Proc. 8 (2000).
  10. A. Henrot, Minimization problems for eigenvalues of the Laplacian. J. Evol. Eq. 3 (2003) 443-461 [MathSciNet].
  11. A. Henrot and E. Oudet, Le stade ne minimise pas $% \lambda _{2}$ parmi les ouverts convexes du plan. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 417-422 [MathSciNet].
  12. A. Henrot and E. Oudet, Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions. Arch. Ration. Mech. Anal. 169 (2003) 73-87 [MathSciNet].
  13. A. Henrot and M. Pierre, Optimisation de forme (in preparation).
  14. E. Krahn, Über eine von Rayleigh formulierte Minimaleigenshaft des Kreises. Math. Ann. 94 (1925) 97-100.
  15. E. Krahn, Über Minimaleigenshaften der Kugel in drei und mehr Dimensionen. Acta Comm. Univ. Dorpat. A9 (1926) 1-44.
  16. S. Osher and F. Santosa, Level set methods for optimization problems involving geometry and constraints: frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171 (2001) 272-288 [CrossRef] [MathSciNet].
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  18. E. Oudet, $\emph{Quelques}$ résultats en optimisation de forme et stabilisation. Prépublication de l'Institut de recherche mathématique avancée, Strasbourg (2002).
  19. M. Pierre and J.M. Roche, Numerical simulation of tridimensional electromagnetic shaping of liquid metals. Numer. Math. 65 (1993) 203-217 [MathSciNet].
  20. G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics. Ann. Math. Stud. 27 (1952).
  21. J.A. Sethian, Level Set Methods and Fast Marching Methods. Cambridge University Press (1999).
  22. J. Sokolowski and J.P. Zolesio, Introduction to shape optimization: shape sensitivity analysis. Springer, Berlin, Springer Ser. Comput. Math. 10 (1992).
  23. B.A. Troesch, Elliptical membranes with smallest second eigenvalue. Math. Comp. 27 (1973) 767-772.
  24. S.A. Wolf and J.B. Keller, Range of the first two eigenvalues of the laplacian. Proc. Roy. Soc. Lond. A 447 (1994) 397-412.



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