國立虎尾科技大學 |

Optimal transport for applied mathematicians = calculus of variations, PDEs, and modeling /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Optimal transport for applied mathematicians/ by Filippo Santambrogio.
Reminder of title:	calculus of variations, PDEs, and modeling /
Author:	Santambrogio, Filippo.
Published:	Cham :Imprint: Birkhauser, : 2015.,
Description:	xxvii, 353 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Measure and Integration. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-20828-2
ISBN:	9783319208282

Optimal transport for applied mathematicians = calculus of variations, PDEs, and modeling /
Santambrogio, Filippo.

Optimal transport for applied mathematicianscalculus of variations, PDEs, and modeling /[electronic resource] :by Filippo Santambrogio. - Cham :Imprint: Birkhauser,2015. - xxvii, 353 p. :ill., digital ;24 cm. - Progress in nonlinear differential equations and their applications,v.871421-1750 ;. - Progress in nonlinear differential equations and their applications ;v.83..

This 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.

ISBN: 9783319208282

Standard No.: 10.1007/978-3-319-20828-2doiSubjects--Topical Terms:

672015
Measure and Integration.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Optimal transport for applied mathematicians = calculus of variations, PDEs, and modeling /
LDR:02278nam a2200337 a 4500 001 838604
003 DE-He213
005 20160413154355.0
006 m d
007 cr nn 008maaau
008 160616s2015 gw s 0 eng d
020 $a 9783319208282 $q (electronic bk.)
020 $a 9783319208275 $q (paper)
024 7 $a 10.1007/978-3-319-20828-2 $2 doi
035 $a 978-3-319-20828-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.5
072 7 $a PBKQ $2 bicssc
072 7 $a PBU $2 bicssc
072 7 $a MAT005000 $2 bisacsh
072 7 $a MAT029020 $2 bisacsh
082 0 4 $a 519.6 $2 23
090 $a QA402.5 $b .S232 2015
100 1 $a Santambrogio, Filippo. $3 1069842
245 1 0 $a Optimal transport for applied mathematicians $h [electronic resource] : $b calculus of variations, PDEs, and modeling / $c by Filippo Santambrogio.
260 $a Cham : $c 2015. $b Imprint: Birkhauser, $b Springer International Publishing :
300 $a xxvii, 353 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in nonlinear differential equations and their applications, $x 1421-1750 ; $v v.87
520 $a This 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 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 1 4 $a Mathematics. $3 527692
650 0 $a Differential equations, Partial. $3 527784
650 0 $a Mathematical optimization. $3 527675
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Progress in nonlinear differential equations and their applications ; $v v.83. $3 888907
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-20828-2
950 $a Mathematics and Statistics (Springer-11649)