Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T02:07:41.591Z Has data issue: false hasContentIssue false

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

from PART 1 - SHORT COURSES

Published online by Cambridge University Press:  05 August 2014

By
Filippo Santambrogio
Edited by
Yann Ollivier ,
Hervé Pajot  and
Cedric Villani
Filippo Santambrogio
Affiliation:
France
Yann Ollivier
Affiliation:
Université de Paris XI
Hervé Pajot
Affiliation:
Université de Grenoble
Cedric Villani
Affiliation:
Université de Paris VI (Pierre et Marie Curie)
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Optimal Transport
Theory and Applications
 , pp. 22 - 40
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] M., Beckmann, A continuous model of transportation, Econometrica (20), 643–660, 1952.Google Scholar
[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.Google Scholar
[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.Google Scholar
[8] Y., Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. (44), no. 4, 375–417, 1991.Google Scholar
[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.Google Scholar
[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.Google Scholar
[11] G., Carlier and I., Ekeland, The structure of cities, J. Global Optim. (29), 371–376, 2004.Google Scholar
[12] G., Carlier and I., Ekeland, Equilibrium structure of a bidimensional asymmetric city. Nonlinear Anal. Real World Appl. (8), no. 3, 725–748, 2007.Google Scholar
[13] G., Carlier, C., Jimenez, and F., Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria, SIAM J. Control Optim. (47), 1330–1350, 2008.Google Scholar
[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.Google Scholar
[15] G., Carlier and F., Santambrogio, A variational model for urban planning with traffic congestion, ESAIM Control Optim. Calc. Var. (11), 595–613, 2007.Google Scholar
[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.Google Scholar
[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.Google Scholar
[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.Google Scholar
[19] J.-M., Lasry and P.-L., Lions, Mean-field games, Japan. J. Math. (2), 229–260, 2007.Google Scholar
[20] H., Hotelling, Stability in competition, Econ. J. (39), 41–57, 1929.Google Scholar
[21] J.-C., Rochet and P., Chone, Ironing, sweeping and multidimensional screening, Econometrica (66), no. 4, 783–826, 1998.Google Scholar
[22] F., Santambrogio, Transport and concentration problems with interaction effects, J. Global Optim. (38), no. 1, 129–141, 2007.Google Scholar
[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.Google Scholar
[25] J.G., Wardrop, Some theoretical aspects of road traffic research, Proc. Inst. Civ. Eng., (2), no. 2, 325-378, 1952.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×