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-gbm5v Total loading time: 0 Render date: 2024-12-23T02:07:57.336Z Has data issue: false hasContentIssue false

1 - Introduction to optimal transport theory

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. 3 - 21
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] L., Ambrosio, Lecture notes on optimal transport problems, Mathematical Aspects of Evolving Interfaces, Springer Verlag, Berlin, Lecture Notes in Mathematics (1812), 1-52, 2003.
[2] L., Ambrosio, N., Gigli and G., Savare, Gradient Flows in Metric Spaces and in the Spaces of Probability Measures. Lectures in Mathematics, ETH Zurich, Birkhauser, 2005.
[3] L., Ambrosio and A., Fratelli. Existence and stability results in the L1 theory of optimal transportation, in Optimal Transportation and Applications, Lecture Notes in Mathematics (CIME Series, Martina Franca, 2001) 1813, L.A., Caffarelli and S., Salsa (eds), 123-160, 2003.
[4] L., Ambrosio and F., Tilli, Topics on Analysis in Metric Spaces. Oxford Lecture Series in Mathematics and its Applications (25). Oxford University Press, Oxford, 2004.
[5] M., Beckmann, A continuous model of transportation, Econometrica (20), 643-660, 1952.
[6] Y., Brenier, Ducomposition polaire et rearrangement monotone des champs de vecteurs. C. R. Acad. Sci. Paris Ser. I Math. (305), no. 19, 805-808, 1987.
[7] L., Caffarelli, A localization property of viscosity solutions to the Monge-Ampere equation and their strict convexity. Ann. Math. (131), no. 1, 129-134, 1990.
[8] L., Caffarelli, Interior W2,p estimates for solutions of the Monge-Ampere equation. Ann. Math. (131), no. 1, 135-150, 1990.
[9] L., Caffarelli, Some regularity properties of solutions of Monge Ampere equation. Comm. Pure Appl. Math. (44), no. 8-9, 965-969, 1991.
[10] T., Champion, L. De, Pascale, F., Juutinen, The oo-Wasserstein distance: local solutions and existence of optimal transport maps, SIAM J. Math. An. (40), no. 1, 1-20, 2008.Google Scholar
[11] C., Jimenez, Optimisation de problemes de transport, PhD thesis, Universite du Sud-Toulon-Var, 2005.
[12] L., Kantorovich, On the transfer of masses. Dokl. Acad. Nauk. USSR, (37), 7-8, 1942.Google Scholar
[13] R. J., McCann, A convexity principle for interacting gases. Adv. Math. (128), no. 1, 153-159, 1997.Google Scholar
[14] G., Monge, Mumoire sur la thüorie des düblais et des remblais, Histoire de l'Académie Royale des Sciences de Paris, 666-704, 1781.
[15] C., Villani. Topics in Optimal Transportation. Graduate Studies in Mathematics, AMS, 2003.
[16] C., Villani, Optimal Transport: Old and New, Springer Verlag (Grundlehren der mathematischen Wissenschaften), 2008.

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
×