000			02118nam a2200241 4500
005			20250403170841.0
008			250403b |||||||| |||| 00| 0 eng d
020			_a9781470425623
037			_cTextual
040			_aRTL _cRTL
084			_aX4 P3 _qRTL
100			_aVillani, Cedric. _9459232
245			_aTopics in optimal transportation
260			_aProvidence _bAmerican Mathematical Society _c2003
300			_axiv, 370p. _bIncludes bibliography and index
440			_vVol. 58
490			_aGraduate studies in mathematics
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			_aMonge-Ampère equations _9751828
650			_aTransportation problems (Programming) _9751829
650			_aMathematics
942			_2CC _n0 _cTB _hX4 P3
999			_c1308453 _d1308453