Readers are only assumed to be familiar with the basics of measure theory and functional analysis. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. 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. Perhaps paradoxical to some, both disciplines are concerned with describing the world around us, understanding its parts. In the words of the great poet Senghor, Cedric Villani makes the bold claim that Mathematics is the Poetry of Science. 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.Įach of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. 12.51 - 16.95 5 Used from 12.51 19 New from 13.16. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. 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 a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. This is the first comprehensive introduction to the theory of mass transportation with its many-and sometimes unexpected-applications.
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