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_a9783319208282 _9978-3-319-20828-2 |
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024 | 7 |
_a10.1007/978-3-319-20828-2 _2doi |
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_aSpringer _cSpringer _dRU-ToGU |
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_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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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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 |
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650 | 0 |
_aMeasure theory. _9461133 |
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650 | 0 |
_aDifferential Equations. _9303496 |
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_aPartial Differential Equations. _9303602 |
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650 | 0 |
_aCalculus of variations. _9421215 |
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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 |
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_aSpringerLink (Online service) _9143950 |
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_aProgress in Nonlinear Differential Equations and Their Applications, _9307379 |
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