TY  - BOOK
AU  - Villani, Cedric
TI  - Topics in optimal transportation
T2  - Graduates Studies in Mathematics ; 
SN  - 9781470425623
U1  - 519.72 VIL 
PY  - 2003///
CY  - Hyderabad : 
PB  - American Mathematical Society, 
KW  - Transportation Problems
KW  - Monge-Ampere equations
N1  - Includes index
N2  - Cedric Villani's book is a lucid and very readable documentation of the tremendous recent analytic progress in ``optimal mass transportation'' theory and of its diverse and unexpected applications in optimization, nonlinear PDE, geometry, and mathematical physics. --Lawrence C. Evans, University of California at Berkeley 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
ER  -