Open Access
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S6
Number of page(s) 32
Published online 01 March 2021
  1. D. Bucur and G. Buttazzo, Variational methods in shape optimization problems, Vol. 65 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston, Inc., Boston, MA (2005). [CrossRef] [Google Scholar]
  2. G. Buttazzo and G. Dal Maso An existence result for a class of shape optimization problems. Arch. Rational Mech. Anal. 122 (1993) 183–195. [Google Scholar]
  3. Y. Chen, L. Wu, A.M. Society and B. Hu, Second Order Elliptic Equations and Elliptic Systems. Translations of Mathematical Monographs. American Mathematical Society (1998). [Google Scholar]
  4. R. Cominetti and J.-P. Penot, Tangent sets to unilateral convex sets. C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 1631–1636. [Google Scholar]
  5. M. Dambrine and J. Lamboley. Stability in shape optimization with second variation. J. Diff. Equ. 267 (2019) 3009–3045. [Google Scholar]
  6. M. Dambrine and M. Pierre, About stability of equilibrium shapes. ESAIM: M2AN 34 (2000) 811–834. [CrossRef] [EDP Sciences] [Google Scholar]
  7. M.C. Delfour and J.P. Zolésio, Shapes and geometries, Vol. 22 of Advances in Design and Control, second edition. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
  8. A. Evgrafov, The limits of porous materials in the topology optimization of Stokes flows. Appl. Math. Optim. 52 (2005) 263–277. [Google Scholar]
  9. R.A. Feijóo, A.A. Novotny, E. Taroco and C. Padra, The topological derivative for the Poisson’s problem. Math. Models Methods Appl. Sci. 13 (2003) 1825–1844. [Google Scholar]
  10. M. Hayouni, Lipschitz continuity of the state function in a shape optimization problem. J. Convex Anal. 6 (1999) 71–90. [Google Scholar]
  11. A. Henrot, Extremum problems for eigenvalues of elliptic operators, in Frontiers in Mathematics. Birkhäuser Verlag, Basel (2006). [CrossRef] [Google Scholar]
  12. A. Henrot (Ed.), Shape Optimization and Spectral Theory. De Gruyter Open, Warsaw (2017). [CrossRef] [Google Scholar]
  13. A. Henrot and M. Pierre, Variation et optimisation de formes: une analyse géométrique, Vol. 48. Springer Science & Business Media (2006). [Google Scholar]
  14. A. Henrot, M. Pierre and M. Rihani, Positivity of the shape Hessian and instability of some equilibrium shapes. Mediterr. J. Math. 1 (2004) 195–214. [Google Scholar]
  15. M. Iguernane, S. Nazarov, J.-R. Roche, J. Sokolowski and K. Szulc, Topological derivatives for semilinear elliptic equations. Int. J. Appl. Math. Comput. Sci. 19 (2009) 191–205. [CrossRef] [Google Scholar]
  16. B. Kawohl, Rearrangements and convexity of level sets in PDE, Vol. 1150 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (1985). [CrossRef] [Google Scholar]
  17. B. Kawohl, O. Pironneau, L. Tartar and J.-P. Zolésio, Optimal shape design, Centro Internazionale Matematico Estivo (C.I.M.E.), Florence (2000). Lectures given at the Joint C.I.M./C.I.M.E. Summer School held in Tróia, June 1–6, 1998, edited by A. Cellina and A. Ornelas, Fondazione CIME/CIME Foundation Subseries. Vol. 1740 of Lecture Notes in Mathematics. Springer-Verlag, Berlin. [Google Scholar]
  18. I. Mazari, G. Nadin and Y. Privat, Optimal location of resources maximizing the total population size in logistic models. J. Math. Appl. 134 (2020) 1–35. [Google Scholar]
  19. A.A. Novotny and J. Sokołowski, Topological Derivatives in Shape Optimization. Springer, Berlin, Heidelberg (2013). [CrossRef] [Google Scholar]
  20. E. Russ, B. Trey and B. Velichkov, Existence and regularity of optimal shapes for elliptic operators with drift. Calc. Variations Partial Differ. Equ. 58 (2019) 199. [Google Scholar]
  21. G. Talenti, Nonlinear elliptic equations, rearrangements of functions and orlicz spaces. Ann. Math. Pura Appl. 120 (1979) 159–184. [Google Scholar]
  22. B. Velichkov, Existence and Regularity Results for Some Shape Optimization Problems. Scuola Normale Superiore (2015). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.