Lectures on optimal transport / Luigi Ambrosio, Elia Brué, Daniele Semola.
Ambrosio, Luigi, author.; Brué, Elia, author.; Semola, Daniele, author.
2021
QA402.5
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Title Lectures on optimal transport / Luigi Ambrosio, Elia Brué, Daniele Semola.
Author Ambrosio, Luigi, author.
ISBN 9783030721626 (electronic bk.)
3030721620 (electronic bk.)
3030721612
9783030721619
DOI https://doi.org/10.1007/978-3-030-72162-6
Publication Details Cham, Switzerland : Springer, 2021.
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-72162-6 doi
Call Number QA402.5
Dewey Decimal Classification 519.6
Summary This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed July 30, 2021).
Added Author Brué, Elia, author.
Semola, Daniele, author.
Series Unitext ; 130. 2038-5722
Available in Other Form Lectures on optimal transport.
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1 Lecture 1: Preliminary notions and the Monge problem
2 Lecture 2: The Kantorovich problem
3 Lecture 3: The Kantorovich - Rubinstein duality
4 Lecture 4: Necessary and sufficient optimality conditions
5 Lecture 5: Existence of optimal maps and applications
6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport
7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds
8 Lecture 8: The metric side of Optimal Transport
9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport
10 Lecture 10: Wasserstein geodesics, nonbranching and curvature
11 Lecture 11: Gradient flows: an introduction
12 Lecture 12: Gradient flows: the Brézis-Komura theorem
13 Lecture 13: Examples of gradient flows in PDEs
14 Lecture 14: Gradient flows: the EDE and EDI formulations
15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space
16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup
17 Lecture 17: The Benamou-Brenier formula
18 Lecture 18: An introduction to Otto's calculus
19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature.

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