 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
|
|
Lectures on Optimal Transport, Second Edition 2024
出版済み 3週間でお届けいたします。
Title: Lectures on Optimal Transport, Second Edition 2024 Series: La Matematica per il 3+2 Author: Ambrosio, Luigi / Brue, Elia / Semola, Daniele Publisher: Springer ISBN: 9783031768330 Cover: PAPERBACK Date: 2024年12月 DESCRIPTION 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. This is the second edition of the book, first published in 2018. It includes refinement of proofs, an updated bibliography and a more detailed discussion of minmax principles, with the aim of giving two fully self-contained proofs of Kantorovich duality. TABLE OF CONTENTS Lecture I: Preliminary Notions and the Monge Problem Lecture II: The Kantorovich Problem Lecture III: The Kantorovich-Rubinstein Duality Lecture IV: Necessary and Sufficient Optimality Conditions Lecture V: Existence of Optimal Maps and Applications Lecture VI: A Proof of the Isoperimetric Inequality and Stability in Optimal Transport Lecture VII: The Monge-Ampere Equation and Optimal Transport on Riemannian Manifolds Lecture VIII: The Metric Side of Optimal Transport Lecture IX: Analysis on Metric Spaces and the Dynamic Formulation of Optimal Transport Lecture X: Wasserstein Geodesics, Nonbranching and Curvature Lecture XI: Gradient Flows: An Introduction Lecture XII: Gradient Flows: The Brezis-Komura Theorem Lecture XIII: Examples of Gradient Flows in PDEs Lecture XIV: Gradient Flows: The EDE and EDI Formulations Lecture XV: Semicontinuity and Convexity of Energies in the Wasserstein Space Lecture XVI: The Continuity Equation and the Hopf-Lax Semigroup Lecture XVII: The Benamou-Brenier Formula Lecture XVIII: An Introduction to Otto’s Calculus Lecture XIX: Heat Flow, Optimal Transport and Ricci Curvature 最近チェックした商品
5,758円(税523円)
34,679円(税3,152円)
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
