Free Access
Volume 23, Number 1, January-March 2017
Page(s) 309 - 335
Published online 13 December 2016
  1. M. Bernot, V. Caselles and J.-M. Morel, T. plans. Publ. Mat. 49 (2005) 417–451. [CrossRef] [MathSciNet]
  2. M. Bernot, V. Caselles and J.-M. Morel, The structure of branched transportation networks. Calc. Var. Partial Differ. Eq. 32 (2008) 279–317. [CrossRef]
  3. M. Bernot, V. Caselles and J.-M. Morel, Optimal transportation networks: models and theory. Vol. 1955. Springer Science & Business Media (2009).
  4. F. Bethuel, A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces. Preprint arXiv:1401.1649 (2014).
  5. G. Bouchitté and P. Seppecher, Cahn and Hilliard fluid on an oscillating boundary. In Motion by mean curvature and related topics (Trento, 1992). De Gruyter, Berlin (1994) 23–42.
  6. G. Bouchitté, C. Dubs and P. Seppecher, Transitions de phases avec un potentiel dégénéré à l’infini, application à l’équilibre de petites gouttes. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996) 1103–1108.
  7. J. Bourgain and H. Brezis, On the equation div Y = f and application to control of phases. J. Amer. Math. Soc. 16 (2003) 393–426. [CrossRef] [MathSciNet]
  8. A. Braides, Γ-convergence for beginners. Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002).
  9. L. Brasco, G. Buttazzo and F. Santambrogio, A Benamou-Brenier approach to branched transport. SIAM J. Math. Anal. 43 (2011) 1023–1040. [CrossRef] [MathSciNet]
  10. J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. i. interfacial free energy. J. Chem. Phys. 28 (1958) 258–267. [CrossRef]
  11. G. Dal Maso, An introduction to Γ-convergence. Vol. 8 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston, Inc., Boston, MA (1993).
  12. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975) 842–850. [MathSciNet]
  13. C. Dubs, Problèmes de perturbations singulières avec un potentiel dégénéré à l’infini. Ph.D. thesis, Université de Toulon et du Var (1998).
  14. E.N. Gilbert, Minimum cost communication networks. Bell Syst. Tech. J. 46 (1967) 2209–2227. [CrossRef]
  15. F. Maddalena, S. Solimini and J.-M. Morel, A variational model of irrigation patterns. Interfaces Free Bound. 5 (2003) 391–415. [CrossRef] [MathSciNet]
  16. L. Modica and S. Mortola, Un esempio di γ-convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285–299. [MathSciNet]
  17. J.-M. Morel and F. Santambrogio, Comparison of distances between measures. Appl. Math. Lett. 20 (2007) 427–432. [CrossRef]
  18. E. Oudet and F. Santambrogio, A Modica–Mortola approximation for branched transport and applications. Arch. Ration. Mech. Anal. 201 (2011) 115–142. [CrossRef]
  19. P. Pegon, Equivalence between branched transport models by Smirnov decomposition. To appear in RICAM (2017).
  20. F. Santambrogio, A Modica–Mortola approximation for branched transport. C. R. Math. Acad. Sci. Paris 348 (2010) 941–945. [CrossRef] [MathSciNet]
  21. F. Santambrogio, Optimal transport for applied mathematicians. Calculus of variations, PDEs and modeling. Vol. 87 (2015).
  22. C. Villani, Topics in optimal transportation. Number 58 in Graduate Studies in Mathematics. American Mathematical Society, cop. (2003).
  23. Q. Xia, Optimal paths related to transport problems. Commun. Contemp. Math. 5 (2003) 251–279. [CrossRef] [MathSciNet]
  24. Q. Xia, Interior regularity of optimal transport paths. Calc. Var. Partial Differ. Eq. 20 (2004) 283–299. [CrossRef]

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