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] [Google Scholar]
  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] [Google Scholar]
  3. M. Bernot, V. Caselles and J.-M. Morel, Optimal transportation networks: models and theory. Vol. 1955. Springer Science & Business Media (2009). [Google Scholar]
  4. F. Bethuel, A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces. Preprint arXiv:1401.1649 (2014). [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  8. A. Braides, Γ-convergence for beginners. Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  13. C. Dubs, Problèmes de perturbations singulières avec un potentiel dégénéré à l’infini. Ph.D. thesis, Université de Toulon et du Var (1998). [Google Scholar]
  14. E.N. Gilbert, Minimum cost communication networks. Bell Syst. Tech. J. 46 (1967) 2209–2227. [CrossRef] [Google Scholar]
  15. F. Maddalena, S. Solimini and J.-M. Morel, A variational model of irrigation patterns. Interfaces Free Bound. 5 (2003) 391–415. [CrossRef] [MathSciNet] [Google Scholar]
  16. L. Modica and S. Mortola, Un esempio di γ-convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285–299. [MathSciNet] [Google Scholar]
  17. J.-M. Morel and F. Santambrogio, Comparison of distances between measures. Appl. Math. Lett. 20 (2007) 427–432. [CrossRef] [Google Scholar]
  18. E. Oudet and F. Santambrogio, A Modica–Mortola approximation for branched transport and applications. Arch. Ration. Mech. Anal. 201 (2011) 115–142. [CrossRef] [Google Scholar]
  19. P. Pegon, Equivalence between branched transport models by Smirnov decomposition. To appear in RICAM (2017). [Google Scholar]
  20. F. Santambrogio, A Modica–Mortola approximation for branched transport. C. R. Math. Acad. Sci. Paris 348 (2010) 941–945. [CrossRef] [MathSciNet] [Google Scholar]
  21. F. Santambrogio, Optimal transport for applied mathematicians. Calculus of variations, PDEs and modeling. Vol. 87 (2015). [Google Scholar]
  22. C. Villani, Topics in optimal transportation. Number 58 in Graduate Studies in Mathematics. American Mathematical Society, cop. (2003). [Google Scholar]
  23. Q. Xia, Optimal paths related to transport problems. Commun. Contemp. Math. 5 (2003) 251–279. [CrossRef] [MathSciNet] [Google Scholar]
  24. Q. Xia, Interior regularity of optimal transport paths. Calc. Var. Partial Differ. Eq. 20 (2004) 283–299. [CrossRef] [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.