Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- PART 1 SHORT COURSES
- 1 Introduction to optimal transport theory
- 2 Models and applications of optimal transport in economics, traffic, and urban planning
- 3 Logarithmic Sobolev inequality for diffusion semigroups
- 4 Lecture notes on variational models for incompressible Euler equations
- 5 Ricci flow: the foundations via optimal transportation
- 6 Lecture notes on gradient flows and optimal transport
- 7 Ricci curvature, entropy, and optimal transport
- PART 2 SURVEYS AND RESEARCH PAPERS
- References
1 - Introduction to optimal transport theory
from PART 1 - SHORT COURSES
Published online by Cambridge University Press: 05 August 2014
Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- PART 1 SHORT COURSES
- 1 Introduction to optimal transport theory
- 2 Models and applications of optimal transport in economics, traffic, and urban planning
- 3 Logarithmic Sobolev inequality for diffusion semigroups
- 4 Lecture notes on variational models for incompressible Euler equations
- 5 Ricci flow: the foundations via optimal transportation
- 6 Lecture notes on gradient flows and optimal transport
- 7 Ricci curvature, entropy, and optimal transport
- PART 2 SURVEYS AND RESEARCH PAPERS
- References
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- Optimal TransportTheory and Applications, pp. 3 - 21Publisher: Cambridge University PressPrint publication year: 2014
References
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[3] and . 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, and (eds), 123-160, 2003.
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[7] , A localization property of viscosity solutions to the Monge-Ampere equation and their strict convexity. Ann. Math. (131), no. 1, 129-134, 1990.
[8] , Interior W2,p estimates for solutions of the Monge-Ampere equation. Ann. Math. (131), no. 1, 135-150, 1990.
[9] , Some regularity properties of solutions of Monge Ampere equation. Comm. Pure Appl. Math. (44), no. 8-9, 965-969, 1991.
[10] , , , 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] , Optimisation de problemes de transport, PhD thesis, Universite du Sud-Toulon-Var, 2005.
[13] , A convexity principle for interacting gases. Adv. Math. (128), no. 1, 153-159, 1997.Google Scholar
[14] , Mumoire sur la thüorie des düblais et des remblais, Histoire de l'Académie Royale des Sciences de Paris, 666-704, 1781.
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[16] , Optimal Transport: Old and New, Springer Verlag (Grundlehren der mathematischen Wissenschaften), 2008.
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