Topics in Optimal Transportation (Graduate Studies in Mathematics) - Softcover

Cedric Villani (author)

Softcover

ISBN 10: 1470467267 ISBN 13: 9781470467265

Publisher: American Mathematical Society, 2003

Synopsis

In 1781, Gaspard Monge defined the problem of ""optimal transportation"", or the transferring of mass with the least possible amount of work, with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind.

Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology.

Originating from a graduate course, the present volume is at once an introduction to the field of optimal transportation and a survey of the research on the topic over the last 15 years. The book is intended for graduate students and researchers, and it covers both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

About this title

About the Author

Cedric Villani, Ecole Normale Superieure de Lyon, France.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2003
• Language: English
• ISBN 10: 1470467267
• ISBN 13: 9781470467265
• Binding: Paperback
• Number of pages: 370