On the dimension of an irrigable measure
Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007), pp. 1-49. 
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Devillanova, Giuseppe; Solimini, Sergio. On the dimension of an irrigable measure. Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007), pp. 1-49. http://www.numdam.org/item/RSMUP_2007__117__1_0/

[1] L. Ambrosio, Lecture Notes on Optimal Transport Problems, Scuola Normale Superiore, Pisa, 2000. | MR | Zbl

[2] V. Caselles - J.M. Morel, Irrigation, Proc. of the Int. Workshop on variational methods for discontinuous structures, with applications to image segmentation and continuum mechanics. Edited by Gianni Dal Maso and Franco Tomarelli, July 4-6, Villa Erba, Cernobbio (Como), Italy, 2001. | MR | Zbl

[3] G. Devillanova - S. Solimini, Elementary properties of optimal irrigation patterns, Calculus of Variations, to appear. | MR | Zbl

[4] F. Maddalena - J.M. Morel - S. Solimini, A variational model of irrigation patterns Interfaces and Free Boundaries 5 (2003), pp. 391-415 | MR | Zbl

[5] L.C. Evans, Partial Differential Equations and Monge-Kantorovich Mass Transfer, Current Developments in Mathematics, Int. Press, Boston, MA, 1999. | MR | Zbl

[6] L.C. Evans - R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992. | MR | Zbl

[7] L. Kantorovich, On the transfer of masses, Dokl. Acad. Nauk. USSR, 37 (1942), pp. 7-8.

[8] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces Fractals and rectificability (1995), Gambridge University Press. | MR | Zbl

[9] G. Monge, Mémoire sur la théorie des déblais et de remblais, Historie de l'Académie Royale des Sciences de Paris (1781), pp. 666-704.

[10] Q. Xia, Optimal paths related to transport problems, Commun. Contemp. Math 5, (2003), pp. 251-279. | MR | Zbl