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Abstract:

This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obtain, taking limits in the rescaled nonlocal formulation, the PDE formulation given by Evans-Gangbo for the classical problem. © 2011 Elsevier Inc.

Registro:

Documento: Artículo
Título:A Monge-Kantorovich mass transport problem for a discrete distance
Autor:Igbida, N.; Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Institut de recherche XLIM, UMR-CNRS 6172, Faculté des sciences et techniques, Université de Limoges, France
Departament d'Anàlisi Matemàtica, Universitat de València, València, Spain
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Mass transport; Monge-Kantorovich problems; Nonlocal problems
Año:2011
Volumen:260
Número:12
Página de inicio:3494
Página de fin:3534
DOI: http://dx.doi.org/10.1016/j.jfa.2011.02.023
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
CODEN:JFUAA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00221236_v260_n12_p3494_Igbida.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v260_n12_p3494_Igbida

Referencias:

  • Ambrosio, L., Lecture notes on optimal transport problems (2003) Lecture Notes in Math., 1812, pp. 1-52. , Springer-Verlag, Berlin, Mathematical Aspects of Evolving Interfaces
  • Ambrosio, L., Fusco, N., Pallara, D., Functions of Bounded Variation and Free Discontinuity Problems (2000) Oxford Math. Monogr.
  • Ambrosio, L., Pratelli, A., Existence and stability results in the L1 theory of optimal transportation (2003) Lecture Notes in Math., 1813, pp. 123-160. , Springer-Verlag, Berlin, Optimal Transportation and Applications
  • Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., A nonlocal p-Laplacian evolution equation with Neumann boundary conditions (2008) J. Math. Pures Appl., 90, pp. 201-227
  • Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., The limit as p→∞ in a nonlocal p-Laplacian evolution equation. A nonlocal approximation of a model for sandpiles (2009) Calc. Var. Partial Differential Equations, 35, pp. 279-316
  • Aronsson, G., Evans, L.C., Wu, Y., Fast/slow diffusion and growing sandpiles (1996) J. Differential Equations, 131, pp. 304-335
  • Bouchitté, G., Buttazzo, G., Seppecher, P., Energy with respect to measures and applications to low dimensional structures (1997) Calc. Var. Partial Differential Equations, 5, pp. 37-54
  • Bouchitté, G., Champion, T., Jiminez, C., Completion of the space of measures in the Kantorovich norm (2005) Riv. Mat. Univ. Parma (7), pp. 127-139
  • Caffarelli, L.A., Feldman, M., McCann, R.J., Constructing optimal maps for Monge's transport problem as limit of strictly convex costs (2001) J. Amer. Math. Soc., 15, pp. 1-26
  • Evans, L.C., Partial differential equations and Monge-Kantorovich mass transfer (1999) Current Developments in Mathematics, pp. 65-126. , International Press, Boston, MA
  • Evans, L.C., Gangbo, W., Differential Equation methods in the Monge-Kantorovich mass transfer problem (1999) Mem. Amer. Math. Soc., 137 (653), pp. viii+66
  • De Pascale, L., Pratelli, A., Regularity properties for Monge transport density and for solutions of some shape optimization problem (2002) Calc. Var. Partial Differential Equations, 14, pp. 249-274
  • De Pascale, L., Pratelli, A., Sharp summability for Monge transport density via interpolation (2004) ESAIM Control Optim. Calc. Var., 10, pp. 549-552
  • Igbida, N., Partial integro-differential equation in granular matter and its connection with stochastic model, preprint; Kantorovich, L.V., On the transfer of masses (1942) Dokl. Nauk SSSR, 37, pp. 227-229
  • Pratelli, A., On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation (2007) Ann. Inst. H. Poincaré Probab. Statist., 43, pp. 1-13
  • Rachev, S.T., Rüschendorf, L., (1998) Mass Transportation Problems, , Springer-Verlag
  • Sudakov, V.N., Geometric problems in the theory of infinite-dimensional probability distributions (1979) Proc. Steklov Inst. Math., 141, pp. 1-178
  • Villani, C., Topics in Optimal Transportation (2003) Grad. Stud. Math., 58
  • Villani, C., Optimal Transport, Old and New (2008) Grundlehren Math. Wiss., 338

Citas:

---------- APA ----------
Igbida, N., Mazón, J.M., Rossi, J.D. & Toledo, J. (2011) . A Monge-Kantorovich mass transport problem for a discrete distance. Journal of Functional Analysis, 260(12), 3494-3534.
http://dx.doi.org/10.1016/j.jfa.2011.02.023
---------- CHICAGO ----------
Igbida, N., Mazón, J.M., Rossi, J.D., Toledo, J. "A Monge-Kantorovich mass transport problem for a discrete distance" . Journal of Functional Analysis 260, no. 12 (2011) : 3494-3534.
http://dx.doi.org/10.1016/j.jfa.2011.02.023
---------- MLA ----------
Igbida, N., Mazón, J.M., Rossi, J.D., Toledo, J. "A Monge-Kantorovich mass transport problem for a discrete distance" . Journal of Functional Analysis, vol. 260, no. 12, 2011, pp. 3494-3534.
http://dx.doi.org/10.1016/j.jfa.2011.02.023
---------- VANCOUVER ----------
Igbida, N., Mazón, J.M., Rossi, J.D., Toledo, J. A Monge-Kantorovich mass transport problem for a discrete distance. J. Funct. Anal. 2011;260(12):3494-3534.
http://dx.doi.org/10.1016/j.jfa.2011.02.023