000			01987nam a2200217 4500
005			20190129154327.0
008			190108b xxu||||| |||| 00| 0 eng d
020			_a9781470425623
040			_cIIT Kanpur
041			_aeng
082			_a519.72 _bV712t
100			_aVillani, Cedric
245			_aTopics in optimal transportation _cCedric Villani
260			_aProvidence _bAmerican Mathematical Society _c2003
300			_axiv, 370p
440			_aGraduate studies in mathematics; v.58
520			_aThis is the first comprehensive introduction to the theory of mass transportation with its many--and sometimes unexpected--applications. 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. 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 intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.
650			_aTransportation problems (Programming)
650			_aMonge-Ampere equations
942			_cBK
999			_c560041 _d560041