LEADER 02735nam a2200325 i 4500
001 991003377389707536
008 170530s2015    sz a         |00| 0|eng d
020   $a9783319208275
035   $ab14324623-39ule_inst
082 04$a515.64$223
084   $aAMS 49-02
084   $aLC QA402.5
100 1 $aSantambrogio, Filippo$0742112
245 10$aOptimal transport for applied mathematicians :$bcalculus of variations, PDEs, and modeling /$cFilippo Santambrogio
264  1$aCham :$bSpringer International Publishing,$cc2015
300   $axxvii, 353 p. :$b30 ill., 19 ill. in color ;$c24 cm
490 1 $aProgress in nonlinear differential equations and their applications,$x1421-1750 ;$v87
504   $aIncludes bibliographical references
505 0 $aPreface ; Primal and dual problems ; One-dimensional Issues ; L? L?[subscript] theory ; Minimal flows ; Wasserstein spaces ; Numerical methods ; Functionals over probabilities ; Gradient flows ; Exercises ; References ; Index
520   $aThis monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource
650  0$aMeasure theory
650  0$aPartial differential equations
650  0$aCalculus of variations
830  0$aProgress in nonlinear differential equations and their applications,$x1421-1750 ;$v87
907   $a.b14324623$b05-06-17$c30-05-17
912   $a991003377389707536
945   $aLE013 49-XX SAN11 (2015)$g1$i2013000294766$lle013$op$pE62.39$q-$rl$s-  $t0$u0$v0$w0$x0$y.i15809444$z05-06-17
996   $aOptimal transport for applied mathematicians$91474054
997   $aUNISALENTO
998   $ale013$b30-05-17$cm$da  $e-$feng$gsz $h0$i0