Open Access
Volume 28, 2022
Article Number 27
Number of page(s) 41
Published online 26 May 2022
  1. G. Allaire, Shape optimization by the homogenization method. Vol. 146 of Applied Mathematical Sciences. Springer-Verlag, New York (2002). [CrossRef] [Google Scholar]
  2. G. Allaire and S. Aubry, On optimal microstructures for a plane shape optimization problem. Struct. Optim. 17 (1999) 86–94. [CrossRef] [Google Scholar]
  3. L. Ambrosio and G. Buttazzo, An optimal design problem with perimeter penalization. Calc. Var. Partial Differ. Equ. 1 (1993) 55–69. [CrossRef] [Google Scholar]
  4. R. Choksi, S. Conti, R.V. Kohn and F. Otto, Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor. Commun. Pure Appl. Math. 61 (2008) 595–626. [CrossRef] [Google Scholar]
  5. R. Choksi and R.V. Kohn, Bounds on the micromagnetic energy of a uniaxial ferromagnet. Commun. Pure Appl. Math. 51 (1998) 259–289. [CrossRef] [Google Scholar]
  6. R. Choksi, R.V. Kohn and F. Otto, Domain branching in uniaxial ferromagnets: a scaling law for the minimum energy. Commun. Math. Phys. 201 (1999) 61–79. [CrossRef] [Google Scholar]
  7. R. Choksi, R.V. Kohn and F. Otto, Energy minimization and flux domain structure in the intermediate state of a type-I superconductor. J. Nonlinear Sci. 14 (2004) 119–171. [CrossRef] [MathSciNet] [Google Scholar]
  8. S. Conti and F. Maggi, Confining thin elastic sheets and folding paper. Arch. Ration. Mech. Anal. 187 (2008) 1–48. [Google Scholar]
  9. Y. Grabovsky and R.V. Kohn, Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. i: The confocal ellipse construction. J. Mech. Phys. Solids 43 (1995) 933–947. [CrossRef] [MathSciNet] [Google Scholar]
  10. Y. Grabovsky and R.V. Kohn, Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. ii: The Vigdergauz microstructure. J. Mech. Phys. Solids 43 (1995) 949–972. [CrossRef] [MathSciNet] [Google Scholar]
  11. Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11 (1963) 127–140. [CrossRef] [MathSciNet] [Google Scholar]
  12. R.V. Kohn and S. Muller, Surface energy and microstructure in coherent phase transitions. Commun. Pure Appl. Math. 47 (1994) 405–435. [CrossRef] [Google Scholar]
  13. R.V. Kohn and G. Strang, Optimal design and relaxation of variational problems. I. Commun. Pure Appl. Math. 39 (1986) 113–137. [CrossRef] [Google Scholar]
  14. R.V. Kohn and B. Wirth, Optimal fine-scale structures in compliance minimization for a uniaxial load. Proc. Royal Soc. Lond. A 470 (2014) 1–13. [Google Scholar]
  15. G.W. Milton, The Theory of Composites. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press (2002). [Google Scholar]
  16. A. Ruland and A. Tribuzio, On the energy scaling behaviour of a singularly perturbed tartar square. Arch. Ratl. Mech. Anal. 243 (2022) 401–431. [CrossRef] [Google Scholar]
  17. F. Santambrogio, Optimal Transport for Applied Mathematicians. Birkhäuser Verlag, Basel, 1 edition (2015). [CrossRef] [Google Scholar]
  18. R. Temam and A. Miranville, Mathematical modeling in continuum mechanics. Cambridge University Press, Cambridge, second edition (2005). [CrossRef] [Google Scholar]
  19. H. Vandeparre, M. Pineirua, F. Brau, B. Roman, J. Bico, C. Gay, W. Bao, C.N. Lau, P.M. Reis and P. Damman, Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains. Phys. Rev. Lett. 106 (2011) 224301. [CrossRef] [PubMed] [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.