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.
Rezensionen / Stimmen
"This book is particularly suited for students who desire to learn from a text which closely follows the organization of a course, as well as for researchers and professors looking for inspiration for their own lecturers on the topic. ... The exposition is clear and mostly self-contained, with a nice list of examples that show the necessity of the assumptions of some classical results of the theory." (Nicolo De Ponti, zbMATH 1485.49001, 2022)
"This book is very well written and will be accessible to graduate students without background on optimal transport ... . All in all, this textbook is recommended to graduate students and researchers who want to discover the fundamental theory of optimal transport and its ramifications to several areas of mathematics. It can also easily be used by professors who want to teach a graduate course on the topic." (Hugo Lavenant, Mathematical Reviews, June, 2022)
"This book is particularly suited for students who desire to learn from a text which closely follows the organization of a course, as well as for researchers and professors looking for inspiration for their own lecturers on the topic. ... The exposition is clear and mostly self-contained, with a nice list of examples that show the necessity of the assumptions of some classical results of the theory." (Nicolo De Ponti, zbMATH 1485.49001, 2022)
"This book is very well written and will be accessible to graduate students without background on optimal transport ... . All in all, this textbook is recommended to graduate students and researchers who want to discover the fundamental theory of optimal transport and its ramifications to several areas of mathematics. It can also easily be used by professors who want to teach a graduate course on the topic." (Hugo Lavenant, Mathematical Reviews, June, 2022)
