Lectures on Optimal Transport (Paperback)

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-Ampere 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 Brezis-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.

Luigi Ambrosio (지은이)    정보 더보기

Elia Brue (지은이)    정보 더보기

Daniele Semola (지은이)    정보 더보기

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