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All issues Volume 21 / No 1 (January-March 2015) ESAIM: COCV, 21 1 (2015) 247-270 References
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Issue
ESAIM: COCV
Volume 21, Number 1, January-March 2015
Page(s) 247 - 270
DOI https://doi.org/10.1051/cocv/2014031
Published online 14 January 2015
  1. G. Alberti, R. Choksi and F. Otto, Uniform energy distribution for minimizers of an isoperimetric problem with long-range interactions. J. Amer. Math. Soc. 22 (2009) 569–605. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Alberti and S. Müller, A new approach to variational problems with multiple scales. Commun. Pure Appl. Math. 54 (2001) 761–825. [CrossRef] [MathSciNet] [Google Scholar]
  3. E. Acerbi, N. Fusco and M. Morini, Minimality via second variation for a nonlocal isoperimetric problem, Commun. Math. Phys. 322 (2013) 515–557. [Google Scholar]
  4. V. Bögelein, F. Duzaar and N. Fusco, A quantitative isoperimetric inequality on the sphere. Preprint (2014). [Google Scholar]
  5. T.L. Chantawansri, A.W. Bosse, A. Hexemer, H.D. Ceniceros, C.J. García-Cervera, E.J. Kramer and G.H. Fredrickson, Self-consistent field theory simulations of block copolymers assembly on a sphere. Phys. Rev. E 75 (2007) 031802. [CrossRef] [Google Scholar]
  6. R. Choksi and M.A. Peletier, Small volume fraction limit of the diblock copolymer problem I: Sharp interface functional. SIAM J. Math. Anal. 42 (2010) 1334–1370. [CrossRef] [MathSciNet] [Google Scholar]
  7. R. Choksi and M.A. Peletier, Small volume fraction limit of the diblock copolymer problem II: Diffuse interface functional. SIAM J. Math. Anal. 43 (2011) 739–763. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Choksi and P. Sternberg, On the first and second variations of a nonlocal isoperimetric problem. J. Reine Angew. Math. 611 (2005) 75–108. [Google Scholar]
  9. M. Cicalese and E. Spadaro, Droplet minimizers of an isoperimetric problem with long-range interactions. Commun. Pure Appl. Math. 66 (2013) 1298–1333. [CrossRef] [Google Scholar]
  10. M.P. do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, New Jersey (1976). [Google Scholar]
  11. T. Einert, Grain Boundary Scars on Spherical Crystals. Langmuir 21 (2005) 12076–12079. [CrossRef] [PubMed] [Google Scholar]
  12. B. K. Ganser, et. al., Assembly and Analysis of Conical Models for the HIV-1 Core. Science 80 (1999) 80–83. [CrossRef] [PubMed] [Google Scholar]
  13. S. Gillmor, J. Lee and X. Ren, The role of Gauss curvature in a membrane phase separation problem. Physica D 240 (2011) 1913–1927. [CrossRef] [Google Scholar]
  14. D. Goldman, C.B. Muratov and S. Serfaty, The Gamma-limit of the two-dimensional Ohta−Kawasaki energy. I. Droplet density. Arch. Rat. Mech. Anal. 210 (2013) 581–613. [CrossRef] [Google Scholar]
  15. D. Goldman, C.B. Muratov and S. Serfaty, The Gamma-limit of the two-dimensional Ohta−Kawasaki energy. II. Droplet arrangement at the sharp interface level via the renormalized energy. Arch. Rat. Mech. Anal. 212 (2014) 445–501. [CrossRef] [Google Scholar]
  16. T. Kohyama, D.M. Kroll and G. Gompper, Budding of crystalline domains in fluid membranes. Phys. Rev. E 68 (2003) 061905. [CrossRef] [Google Scholar]
  17. F. Morgan, M. Hutchings and H. Howards, The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature. Trans. Amer. Math. Soc. 352 (2000) 4889–4909. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Morini and P. Sternberg, Cascade of minimizers for a nonlocal isoperimetric problem in thin domains. SIAM J. Math. Anal. 46 (2014) 2033–2051. [CrossRef] [MathSciNet] [Google Scholar]
  19. S. Müller, Singular perturbations as a selection criterion for periodic minimizing sequences. Calc. Var. Partial Differ. Equ. 1 (1993) 169–204. [Google Scholar]
  20. C.B. Muratov, Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions. Commun. Math. Phys. 299 (2010) 45–87. [CrossRef] [Google Scholar]
  21. T. Ohta and K. Kawasaki, Equilibrium morphology of block copolymer melts. Macromolecules 19 (1986) 2621–2632. [CrossRef] [Google Scholar]
  22. M.A. Peletier and M. Veneroni, Stripe patterns in a model for block copolymers. Math. Model. Meth. Appl. Sci. 20 (2010) 843–907. [CrossRef] [Google Scholar]
  23. X. Ren and J. Wei, On energy minimizers of the diblock copolymer problem. Interfaces Free Bound. 5 (2003) 193–238. [CrossRef] [MathSciNet] [Google Scholar]
  24. X. Ren and J. Wei, On the spectra of three dimensional lamellar solutions of the diblock copolymer problem. SIAM J. Math. Anal. 35 (2003) 1–32. [CrossRef] [MathSciNet] [Google Scholar]
  25. X. Ren and J. Wei, Oval shaped droplet solutions in the saturation process of some pattern formation problems. SIAM J. Math. Anal. 70 (2009) 1120–1138. [CrossRef] [Google Scholar]
  26. M. Ritore, Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces. Commun. Anal. Geom. 9 (2001) 1093–1138. [Google Scholar]
  27. E.N. Spadaro, Uniform energy and density distribution: diblock copolymers’ functional. Interfaces Free Bound. 11 (2009) 447–474. [CrossRef] [MathSciNet] [Google Scholar]
  28. P. Sternberg and I. Topaloglu, On the global minimizers of a nonlocal isoperimetric problem in two dimensions. Interfaces Free Bound. 13 (2011) 155–169. [CrossRef] [MathSciNet] [Google Scholar]
  29. P. Tang, F. Qiu, H. Zhang and Y. Yang, Phase separation patterns for diblock copolymers on spherical surfaces: A finite volume method. Phys. Rev. E 72 (2005) 016710. [CrossRef] [Google Scholar]
  30. I. Topaloglu, On a nonlocal isoperimetric problem on the two-sphere. Commun. Pure Appl. Anal. 12 (2013) 597–620. [CrossRef] [MathSciNet] [Google Scholar]
  31. C. Varea, J.L. Aragon and R.A. Barrio, Turing patterns on a sphere. Phys. Rev. E 60 (1999) 4588–4592. [CrossRef] [Google Scholar]
  32. N.K. Yip, Structure of stable solutions of a one-dimensional variational problem. ESAIM: COCV 12 (2006) 721–751. [CrossRef] [EDP Sciences] [Google Scholar]

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