Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds

Annali di Matematica Pura ed Applicata

Volumn 184, Issue 2, 2005, Pages 215-238

  Pratelli, Aldo ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

Mass transportation; Shape optimization; Transport density

Indexed keywords

EID: 24944565638     PISSN: 03733114     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10231-004-0109-5     Document Type: Article

References (16)

1. Ambrosio, L.: Lecture notes on optimal transport problems. In: Mathematical aspects of evolving interfaces. Lecture Notes in Mathematics, Vol. 1812, pp. 1-52. Springer 2003
2. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford: Oxford University Press 2000
3. Bangert. V.: Minimal measures and minimizing closed normal one-currents. Geom. Funct. Anal. 9, 413-427 (1999)
4. Bao, D., Chern, S.S., Shen, Z.: An introduction to Riemann-Finsler geometry. Graduate Texts in Mathematics, Vol. 200. New York: Springer 2000
5. Benamou, J.-D., Brenier, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84, 375-393 (2000)
6. Bouchitté, G., Buttazzo, G.: Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. (JEMS) 3, 139-168 (2001)
7. Bouchitté, G., Buttazzo, G., Seppecher, P.: Shape Optimization Solutions via Monge-Kantorovich Equation. C. R. Acad. Sci. Paris, Sér. I, Math. 324, 1185-1191 (1997)
8. Brenier, Y.: A Homogenized Model for Vortex Sheets. Arch. Ration. Mech. Anal. 138, 319-353 (1997)
9. De Pascale, L.: On a constrained shape optimization problem. Commun. Appl. Anal. 7 (2003)
10. De Pascale, L., Pratelli, A.: Regularity properties for Monge transport density and for solutions of some shape optimization problem. Calc. Var. Partial Differ. Equ. 14, 249-274 (2002)
11. Evans, L.C.: Partial Differential Equations and Monge-Kantorovich Mass Transfer. Current Developments in Mathematics, pp. 65-126, 1997
12. Evans, L.C., Gangbo, W.: Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Mem. Am. Math. Soc. 137 (1999)
13. Fragalà, I., Mantegazza, C.: On some notions of tangent space to a measure. Proc. R. Soc. Edinb., Sect. A, Math. 129, 331-342 (1999)
14. Gangbo, W., McCann, R.J.: The geometry of optimal transportation. Acta Math. 177, 113-161 (1996)
15. Kantorovich, L.V.: On the transfer of masses. Dokl. Akad. Nauk, Ross. Akad. Nauk 37, 227-229 (1942)
16. Kantorovich, L.V.: On a problem of Monge. Usp. Mat. Nauk 3, 225-226 (1948)