Lectures on Optimal Transport
暫譯: 最優運輸講義
Ambrosio, Luigi, Brué, Elia, Semola, Daniele
- 出版商: Springer
- 出版日期: 2024-12-29
- 售價: $2,320
- 貴賓價: 9.5 折 $2,204
- 語言: 英文
- 頁數: 260
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031768337
- ISBN-13: 9783031768330
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商品描述
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.
商品描述(中文翻譯)
這本教科書是針對數學領域的博士生或高年級本科生，特別是對分析、變分法、機率和最優運輸有興趣的學生。這本書源自於第一作者在意大利高等師範學校（Scuola Normale Superiore）的教學經驗，在過去20年中，該校曾多次開設有關最優運輸及其應用的課程。所選擇的主題和工具達到了一個足夠一般且高級的水平，使得對更具體主題感興趣的學生或學者能夠從這本書中獲得探索所需的背景知識。在對古典理論進行了廣泛且詳細的介紹後，書中更具體地關注於幾何和函數不等式的應用以及偏微分方程。
這是本書的第二版，首次出版於2018年。它包括了證明的精煉、更新的參考文獻以及對最小最大原則的更詳細討論，旨在提供兩個完全自足的Kantorovich對偶性證明。
作者簡介
Prof. Luigi Ambrosio is a Professor of Mathematical Analysis, a former student of the Scuola Normale Superiore and presently its Rector. His research interests include calculus of variations, geometric measure theory, optimal transport and analysis in metric spaces. For his scientific achievements, he has been awarded several prizes, in particular the Fermat prize in 2003, the Balzan Prize in 2019, the Riemann Prize in 2023 and the Nemmers Prize in 2024.
Dr. Elia Bruè is an Associate Professor at Bocconi University, Milan, Italy. He earned his PhD from the Scuola Normale Superiore in 2020. His research interests lie in the fields of Geometric Analysis and Partial Differential Equations, with a focus on Ricci curvature, metric geometry, incompressible fluid mechanics, and passive scalars with rough velocity fields.
Dr. Daniele Semola is an Assistant Professor at the University of Vienna. He was a student in Mathematics at the Scuola Normale Superiore, where he earned his PhD degree in 2020. His research interests lie at the interface between geometric analysis and analysis on metric spaces, mainly with a focus on lower curvature bounds.
作者簡介(中文翻譯)
教授Luigi Ambrosio是數學分析的教授，曾是Scuola Normale Superiore的學生，目前擔任該校的校長。他的研究興趣包括變分法、幾何測度論、最佳運輸以及度量空間中的分析。因其科學成就，他獲得了多個獎項，特別是2003年的Fermat獎、2019年的Balzan獎、2023年的Riemann獎以及2024年的Nemmers獎。
博士Elia Bruè是意大利米蘭Bocconi大學的副教授。他於2020年在Scuola Normale Superiore獲得博士學位。他的研究興趣集中在幾何分析和偏微分方程領域，特別是Ricci曲率、度量幾何、不可壓縮流體力學以及具有粗糙速度場的被動標量。
博士Daniele Semola是維也納大學的助理教授。他曾是Scuola Normale Superiore的數學學生，並於2020年獲得博士學位。他的研究興趣位於幾何分析與度量空間分析的交界處，主要集中在下界曲率的研究上。
