Skip to main content Accessibility help
×
Home
  • Print publication year: 2014
  • Online publication date: August 2014

2 - Models and applications of optimal transport in economics, traffic, and urban planning

from PART 1 - SHORT COURSES
[1] M., Beckmann, A continuous model of transportation, Econometrica (20), 643–660, 1952.
[2] M., Beckmann, C., McGuire, and C., Winsten, C., Studies in Economics of Transportation, Yale University Press, New Haven, 1956.
[3] M., Beckmann and T., Puu, Spatial Economics: Density, Potential and Flow, North-Holland, Amsterdam, 1985.
[4] M., Bernot, V., Caselles, and J.-M., Morel, Optimal Transportation Networks, Models and Theory, Lecture Notes in Mathematics, Springer, Vol. 1955, 2008.
[5] G., Bouchitte and G., Buttazzo, New lower semicontinuity results for nonconvex functionals defined on measures, Nonlinear Anal. (15), 679-692, 1990.
[6] G., Buttazzo, Three optimization problems in mass transportation theory. Nons-mooth Mechanics and Analysis, pp. 13-23, Adv. Mech. Math., 12, Springer, New York, 2006.
[7] L., Brasco, G., Carlier, and F., Santambrogio, Congested traffic dynamics, weak flows and very degenerate elliptic equations, J. Math. Pures Appl. (93), no. 6, 652-671, 2010.
[8] Y., Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. (44), no. 4, 375–417, 1991.
[9] G., Buttazzo and F., Santambrogio, A model for the optimal planning of an urban area. SIAM J. Math. Anal. (37), no. 2, 514–530, 2005.
[10] G., Buttazzo and F., Santambrogio, A mass transportation model for the optimal planning of an urban region. SIAM Rev. (51), no. 3, 593–610, 2009.
[11] G., Carlier and I., Ekeland, The structure of cities, J. Global Optim. (29), 371–376, 2004.
[12] G., Carlier and I., Ekeland, Equilibrium structure of a bidimensional asymmetric city. Nonlinear Anal. Real World Appl. (8), no. 3, 725–748, 2007.
[13] G., Carlier, C., Jimenez, and F., Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria, SIAM J. Control Optim. (47), 1330–1350, 2008.
[14] G., Carlier and T., Lachand-Robert, Regularite des solutions d'un probleme variationnel sous contrainte de convexite. C. R. Acad. Sci. Paris Ser. I Math. (332), no. 1, 79–83, 2001.
[15] G., Carlier and F., Santambrogio, A variational model for urban planning with traffic congestion, ESAIM Control Optim. Calc. Var. (11), 595–613, 2007.
[16] L., De Pascale and A., Pratelli, Regularity properties for Monge transport Density and for Solutions of some Shape Optimization Problem, Calc. Var. Par. Diff. Eq. (14), no. 3, 249–274, 2002.
[17] L., De Pascale, L. C., Evans and A., Pratelli, Integral estimates for transport densities, Bull. London Math. Soc. (36), no. 3, 383–385, 2004.
[18] L., De Pascale and A., Pratelli, Sharp summability for Monge transport density via interpolation, ESAIM Control Optim. Calc. Var. (10), no. 4, 549–552, 2004.
[19] J.-M., Lasry and P.-L., Lions, Mean-field games, Japan. J. Math. (2), 229–260, 2007.
[20] H., Hotelling, Stability in competition, Econ. J. (39), 41–57, 1929.
[21] J.-C., Rochet and P., Chone, Ironing, sweeping and multidimensional screening, Econometrica (66), no. 4, 783–826, 1998.
[22] F., Santambrogio, Transport and concentration problems with interaction effects, J. Global Optim. (38), no. 1, 129–141, 2007.
[23] F., Santambrogio, Variational problems in transport theory with mass concentration, PhD thesis, Edizioni della Normale, Birkhauser, 2007.
[24] F., Santambrogio, Absolute continuity and summability of transport densities: simpler proofs and new estimates, Calc. Var. Par. Diff. Eq. (36), no. 3, 343–354, 2009.
[25] J.G., Wardrop, Some theoretical aspects of road traffic research, Proc. Inst. Civ. Eng., (2), no. 2, 325-378, 1952.