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020 _a9783319208282
_9978-3-319-20828-2
024 7 _a10.1007/978-3-319-20828-2
_2doi
035 _ato000560376
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA315-316
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072 7 _aMAT005000
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072 7 _aMAT029020
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082 0 4 _a515.64
_223
100 1 _aSantambrogio, Filippo.
_eauthor.
_9468180
245 1 0 _aOptimal Transport for Applied Mathematicians
_helectronic resource
_bCalculus of Variations, PDEs, and Modeling /
_cby Filippo Santambrogio.
250 _a1st ed. 2015.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2015.
300 _aXXVII, 353 p. 30 illus., 19 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aProgress in Nonlinear Differential Equations and Their Applications,
_x1421-1750 ;
_v87
505 0 _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.    .
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 _amathematics.
_9566183
650 0 _aMeasure theory.
_9461133
650 0 _aDifferential Equations.
_9303496
650 0 _aPartial Differential Equations.
_9303602
650 0 _aCalculus of variations.
_9421215
650 1 4 _aMathematics.
_9566184
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
_9306640
650 2 4 _aOrdinary Differential Equations.
_9303501
650 2 4 _aPartial Differential Equations.
_9303602
650 2 4 _aMeasure and Integration.
_9303749
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aProgress in Nonlinear Differential Equations and Their Applications,
_9307379
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-20828-2
912 _aZDB-2-SMA
999 _c415635