LEADER 04290nam 22007335 450 001 9910300257403321 005 20251116144819.0 010 $a3-319-20828-4 024 7 $a10.1007/978-3-319-20828-2 035 $a(CKB)3710000000521690 035 $a(SSID)ssj0001585394 035 $a(PQKBManifestationID)16263874 035 $a(PQKBTitleCode)TC0001585394 035 $a(PQKBWorkID)14864073 035 $a(PQKB)11179726 035 $a(DE-He213)978-3-319-20828-2 035 $a(MiAaPQ)EBC6315601 035 $a(MiAaPQ)EBC5592187 035 $a(Au-PeEL)EBL5592187 035 $a(OCoLC)1066196906 035 $a(PPN)190530871 035 $a(EXLCZ)993710000000521690 100 $a20151017d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aOptimal Transport for Applied Mathematicians $eCalculus of Variations, PDEs, and Modeling /$fby Filippo Santambrogio 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (XXVII, 353 p. 30 illus., 19 illus. in color.) 225 1 $aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v87 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-20827-6 320 $aIncludes bibliographical references and index. 327 $aPreface -- Primal and Dual Problems -- One-Dimensional Issues -- L^1 and L^infinity Theory -- Minimal Flows -- Wasserstein Spaces -- Numerical Methods -- Functionals over Probabilities -- Gradient Flows -- Exercises -- References -- Index. . 330 $aThis monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource. 410 0$aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v87 606 $aCalculus of variations 606 $aDifferential equations 606 $aDifferential equations, Partial 606 $aMeasure theory 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 615 0$aCalculus of variations. 615 0$aDifferential equations. 615 0$aDifferential equations, Partial. 615 0$aMeasure theory. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aMeasure and Integration. 676 $a519.6 700 $aSantambrogio$b Filippo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0742112 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300257403321 996 $aOptimal transport for applied mathematicians$91474054 997 $aUNINA