Free Access
Issue |
ESAIM: COCV
Volume 22, Number 2, April-June 2016
|
|
---|---|---|
Page(s) | 543 - 561 | |
DOI | https://doi.org/10.1051/cocv/2015028 | |
Published online | 24 March 2016 |
- L. Ambrosio and B. Kirchheim, Currents in metric spaces. Acta Math. 185 (2000) 1–80. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bernot, V. Caselles and J.-M. Morel, Traffic plans. Publ. Mat. 49 (2005) 417–451. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bernot, V. Caselles and J.M. Morel, Are there infinite irrigation trees? J. Math. Fluid Mech. 8 (2006) 311–332. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bernot, V. Caselles and J.-M. Morel,Optimal Transportation Networks, Models and theory. In vol. 1955 of Lect. Notes Math. Springer-Verlag, Berlin (2009). [Google Scholar]
- F. Bethuel, A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces. Preprint 1401.1649 (2014). [Google Scholar]
- S. Bhaskaran and F.J.M. Salzborn, Optimal design of gas pipeline networks. J. Oper. Res. Soc. 30 (1979) 1047–1060. [CrossRef] [Google Scholar]
- A. Brancolini and G. Buttazzo, Optimal networks for mass transportation problems. ESAIM: COCV 11 (2005) 88–101. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Brancolini, G. Buttazzo and F. Santambrogio, Path functionals over Wasserstein spaces. J. Eur. Math. Soc. 8 (2006) 415–434. [CrossRef] [Google Scholar]
- L. Brasco and F. Santambrogio, An equivalent path functional formulation of branched transportation problems. Discrete Contin. Dyn. Syst. 29 (2011) 845–871. [CrossRef] [MathSciNet] [Google Scholar]
- H. Brezis, J.-M. Coron and E.H. Lieb, Harmonic maps with defects. Comm. Math. Phys. 107 (1986) 649–705. [CrossRef] [MathSciNet] [Google Scholar]
- S. Conti, A. Garroni and A. Massaccesi, Lower semicontinuity and relaxation of functionals on one-dimensional currents with multiplicity in a lattice. Preprint (2013). [Google Scholar]
- T. De Pauw and R. Hardt, Rectifiable and flat G chains in a metric space. Amer. J. Math. 134 (2012) 1–69. [CrossRef] [MathSciNet] [Google Scholar]
- A.K. Deb, Least cost design of branched pipe network system. J. Environ. Eng. Division 100 (1974) 821–835. [Google Scholar]
- H. Federer, Geometric measure theory. Die Grundl. Math. Wiss., Band 153. Springer-Verlag, New York Inc. (1969). [Google Scholar]
- E.N. Gilbert, Minimum cost communication networks. Bell Syst. Tech. J. 46 (1967) 2209–2227. [CrossRef] [Google Scholar]
- S.G. Krantz and H.R. Parks, Geometric Integration Theory. Cornerstones. Birkhäuser Boston Inc., Boston, MA (2008). [Google Scholar]
- F. Maddalena and S. Solimini, Transport distances and irrigation models. J. Convex Anal. 16 (2009) 121–152. [Google Scholar]
- F. Maddalena and S. Solimini, Synchronic and asynchronic descriptions of irrigation problems. Adv. Nonlin. Stud. 13 (2013) 583–623. [CrossRef] [Google Scholar]
- 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]
- A. Marchese and A. Massaccesi, The Steiner tree problem revisited through rectifiable G-currents. Adv. Calc. Var. 9 (2016) 19–39. [MathSciNet] [Google Scholar]
- B. Mauroy, M. Filoche, E.R. Weibel and B. Sapoval, An optimal bronchial tree may be dangerous. Nature. 427 (2004) 633–636. [CrossRef] [PubMed] [Google Scholar]
- J.-M. Morel and F. Santambrogio, The regularity of optimal irrigation patterns. Arch. Ration. Mech. Anal. 195 (2010) 499–531. [CrossRef] [MathSciNet] [Google Scholar]
- E. Paolini and E. Stepanov, Optimal transportation networks as flat chains. Interfaces Free Bound. 8 (2006) 393–436. [CrossRef] [MathSciNet] [Google Scholar]
- E. Paolini and E. Stepanov, Existence and regularity results for the Steiner problem. Calc. Var. Partial Differ. Equ. 46 (2013) 837–860. [Google Scholar]
- E. Paolini, E. Stepanov and Y. Teplitskaya, An example of an infinite Steiner tree connecting an uncountable set. Adv. Calc. Var. 8 (2015) 267–290. [CrossRef] [MathSciNet] [Google Scholar]
- E. Paolini and L. Ulivi, The Steiner problem for infinitely many points. Rend. Semin. Mat. Univ. Padova 124 (2010) 43–56. [CrossRef] [MathSciNet] [Google Scholar]
- L. Simon, Lectures on Geometric Measure Theory. In vol. 3 of Proc. of the Centre for Mathematical Analysis. Australian National University Centre for Mathematical Analysis, Canberra (1983). [Google Scholar]
- E.O. Stepanov, Optimization model of transport currents. Problems in mathematical analysis. J. Math. Sci. (N. Y.) 135 (2006) 3457–3484. [CrossRef] [MathSciNet] [Google Scholar]
- G.B. West, J.H. Brown and B.J. Enquist, A general model for the origin of allometric scaling laws in biology. Science 276 (1997) 122–126. [CrossRef] [PubMed] [Google Scholar]
- B. White, Rectifiability of flat chains. Ann. Math.150 (1999) 165–184. [CrossRef] [MathSciNet] [Google Scholar]
- Q. Xia, Optimal paths related to transport problems. Commun. Contemp. Math. 5 (2003) 251–279. [CrossRef] [MathSciNet] [Google Scholar]
- Q. Xia, Interior regularity of optimal transport paths. Calc. Var. Partial Differ. Equ. 20 (2004) 283–299. [Google Scholar]
- Q. Xia, The formation of a tree leaf. ESAIM: COCV 13 (2007) 359–377. [CrossRef] [EDP Sciences] [Google Scholar]
- W.I. Zangwill, Minimum concave cost flows in certain networks. Manag. Sci. 14 (1968) 429–450. [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.