Issue
ESAIM: M2AN
Volume 49, Number 6, November-December 2015
Special Issue - Optimal Transport
Page(s) 1791 - 1832
DOI https://doi.org/10.1051/m2an/2015028
Published online 05 November 2015
  1. L. Ambrosio, Lecture notes on Optimal Transport Problems. Mathematical Aspects of Evolving Interfaces (Funchal, 2000). In vol. 1812 of Lect. Notes Math. Springer, Berlin (2003) 1–52. [Google Scholar]
  2. Y. Brenier, Décomposition polaire et ré arrangement monotone des champs de vecteurs [Polar decomposition and increasing rearrangement of vector fields]. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987) 805–808. [Google Scholar]
  3. D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry. American Mathematical Society (2001). [Google Scholar]
  4. L.A. Caffarelli, M. Feldman and R.J. McCann, Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs. J. Amer. Math. Soc. 15 (2002) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  5. R. Coifman and G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes. Vol. 242 of Lect. Notes Math. Springer-Verlag (1971). [Google Scholar]
  6. G. Devillanova and S. Solimini, On the dimension of an irrigable measure. Rend. Semin. Mat. Univ. Padova 117 (2007) 1–49. [MathSciNet] [Google Scholar]
  7. L.C. Evans and W. Gangbo, Differential equations methods for the Monge−Kantorovich mass transfer problem. Mem. Amer. Math. Soc. 137 (1999) 653. [Google Scholar]
  8. H. Federer, Geometric measure theory. In vol. 153 of Die Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York Inc. (1969). [Google Scholar]
  9. M. Feldman and R.J. McCann, Uniqueness and transport density in Monge’s mass transportation problem. Calc. Var. Partial Differ. Equ. 15 (2002) 81–113. [Google Scholar]
  10. W. Fleming, Flat chains over a finite coefficient group. Trans. Amer. Math. Soc. 121 (1966) 160-186. [CrossRef] [MathSciNet] [Google Scholar]
  11. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [CrossRef] [MathSciNet] [Google Scholar]
  12. T.C. Halsey, Diffusion-Limited Aggregation: A Model for Pattern Formation. Phys. Today 53 (2000) 36–41. [CrossRef] [Google Scholar]
  13. F. Maddalena, S. Solimini and J.M. Morel, A variational model of irrigation patterns, Interfaces and Free Boundaries 5 (2003) 391–416. [Google Scholar]
  14. A. Mas-Colell, M. Whinston and J. Green, Microeconomic Theory. Oxford University Press, New York (1995). [Google Scholar]
  15. P. Meakin, Progress in DLA Research. Physica D 86 (1995) 104–112. [CrossRef] [Google Scholar]
  16. Z.A. Melzak, On the problem of Steiner. Canad. Math. Bull. 4 (1961) 143–148. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Santambrogio, Optimal Channel Networks, Landscape Function and Branched Transport. Interfaces Free Bound. 9 (2007) 149–169. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Simon, Lectures on geometric measure theory. In vol. 3 of Proc. Centre Math. Anal. Australian National University (1983). [Google Scholar]
  19. D.P. Thierry and R. Hardt, Size minimization and approximating problems. Calc. Var. Partial Differ. Equ. 17 (2003) 405–442. [CrossRef] [Google Scholar]
  20. C. Villani, Topics in Mass Transportation. Vol. 58 of AMS Grad. Stud. Math. 58 (2003). [Google Scholar]
  21. C. Villani, Optimal Transport: Old and New. Grundlehren der mathematischen Wissenschaften (2009). [Google Scholar]
  22. B. White, Rectifiability of flat chains. Ann. Math. 150 (1999) 165–184. [CrossRef] [MathSciNet] [Google Scholar]
  23. T.A. Witten and L.M. Sander, Diffusion-Limited Aggregation, A Kinetic Critical Phenomenon. Phys. Rev. Lett. 47 (1981) 1400–1403. [Google Scholar]
  24. Q. Xia, Optimal paths related to transport problems. Commun. Contemp. Math. 5 (2003) 251–279. [CrossRef] [MathSciNet] [Google Scholar]
  25. Q. Xia, Interior regularity of optimal transport paths. Calc. Var. Partial Differential Equ. 20 (2004) 283–299. [Google Scholar]
  26. Q. Xia, An application of optimal transport paths to urban transport networks. Discr. Contin. Dyn. Syst., Supp. (2005) 904–910. [Google Scholar]
  27. Q. Xia, The formation of tree leaf. ESAIM: COCV 13 (2007) 359–377. [CrossRef] [EDP Sciences] [Google Scholar]
  28. Q. Xia, The geodesic problem in quasimetric spaces. J. Geom. Anal. 19 (2009) 452–479. [CrossRef] [MathSciNet] [Google Scholar]
  29. Q. Xia, Boundary regularity of optimal transport paths. Adv. Calc. Var. 4 (2011) 153–174. [MathSciNet] [Google Scholar]
  30. Q. Xia, Numerical simulation of optimal transport paths. In vol. 1, Proc. of the Second International Conference on Computer Modeling and Simulation ICCMS 2010 (2010) 521–525. DOI: 10.1109/ICCMS.2010.30. [Google Scholar]
  31. Q. Xia, Ramified optimal transportation in geodesic metric spaces. Adv. Calc. Var. 4 (2011) 277–307. [MathSciNet] [Google Scholar]
  32. Q. Xia and A. Vershynina, On the transport dimension of measures. SIAM J. Math. Anal. 41 (2010) 2407–2430. [CrossRef] [Google Scholar]
  33. Q. Xia and D. Unger, Diffusion-limited aggregation driven by optimal transportation. Fractals 18 (2010) 1–7. [CrossRef] [MathSciNet] [Google Scholar]
  34. Q. Xia and S. Xu, The exchange value embedded in a transport system. Appl. Math. Optim. 62 (2010) 229–252. [CrossRef] [MathSciNet] [Google Scholar]
  35. Q. Xia and S. Xu, On the ramified optimal allocation problem. Netw. heterog. Media 8 (2013) 591–624. [CrossRef] [MathSciNet] [Google Scholar]
  36. Q. Xia, On landscape functions associated with transport paths. Discr. Contin. Dyn. Syst. A 34 (2014). [Google Scholar]
  37. Q. Xia and C. Salafia, Transport efficiency of the human placenta. J. Coupled Syst. Multiple Dyn. 2 (2014). [Google Scholar]
  38. Q. Xia, C. Salafia and M. Simon, Optimal transport and placental function. Vol. 17 of Interdisciplinary Topics Appl. Math., Modeling and Computational Science. Springer Proc. Math. Stat. Springer (2015). DOI: 10.1007/978-3-319-12307-3-73. [Google Scholar]
  39. Q. Xia and C. Salafia, Human placentas, Optimal transportation and Autism (submitted). [Google Scholar]
  40. M. Yampolsky, C.M. Salafia and O. Shlakhter, Probability distributions of placental morphological measurements and origins of variability of placental shapes. Placenta 34 (2013) 493–6. [CrossRef] [PubMed] [Google Scholar]

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