Lectures on Optimal Transport. 1st ed. 2021

フォーマット:

電子ブック

責任表示:

by Luigi Ambrosio, Elia Brué, Daniele Semola

言語:

英語

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2021

形態:

IX, 250 p. 1 illus. in color : online resource

著者名:

• Ambrosio, Luigi
• Brué, Elia
• Semola, Daniele
• SpringerLink (Online service)

シリーズ名:

La Matematica per il 3+2 ; 130

目次情報:

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

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

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書誌ID:

IT00017084

ISBN:

9783030721626 [3030721620]      
9783030721633 [3030721639]