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010   $a981-9948-67-3
024 7 $a10.1007/978-981-99-4867-3
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035   $a(DE-He213)978-981-99-4867-3
035   $a(CKB)29337882500041
035   $a(EXLCZ)9929337882500041
100   $a20231209d2023      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aOptimal Transport and Applications to Geometric Optics /$fby Cristian E. Gutiérrez
205   $a1st ed. 2023.
210  1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023.
215   $a1 online resource (140 pages)
225 1 $aSpringerBriefs on PDEs and Data Science,$x2731-7609
311 08$aPrint version: Gutiérrez, Cristian E. Optimal Transport and Applications to Geometric Optics Singapore : Springer,c2024 9789819948666 
327   $aChapter 1 Introduction -- Chapter 2 The normal mapping or subdifferential.-Chapter 3 Sinkhorn?s theorem and application to the distribution problem -- Chapter4 Monge-Kantorovich distance -- Chapter 5 Multivalued measure preserving maps -- Chapter 6 Kantorovich Dual Problem -- Chapter 7 Brenier and Aleksandrov solutions -- Chapter 8 Cyclical monotonicity -- Chapter 9 Quadratic cost -- Chapter 10 Brenier ?s Polar Factorization Theorem -- Chapter 11 Benamou and Brenier formula -- Chapter 12 Snell?s law of refraction -- Chapter 13 Solution of the far field refractor problem < 1 -- Chapter 14 Proof of the Disintegration Theorem -- Chapter 15 Acknowledgements -- Chapter 16 References.
330   $aThis book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.
410  0$aSpringerBriefs on PDEs and Data Science,$x2731-7609
606   $aOptimització matemàtica$2thub
606   $aMathematical optimization
606   $aOperations research
606   $aManagement science
606   $aGeometrical optics
606   $aWave theory of light
606   $aDifferential equations
606   $aOptimization
606   $aOperations Research, Management Science 
606   $aClassical Optics, Geometric and Wave optics
606   $aDifferential Equations
608   $aLlibres electrònics$2thub
615  7$aOptimització matemàtica
615  0$aMathematical optimization.
615  0$aOperations research.
615  0$aManagement science.
615  0$aGeometrical optics.
615  0$aWave theory of light.
615  0$aDifferential equations.
615 14$aOptimization.
615 24$aOperations Research, Management Science .
615 24$aClassical Optics, Geometric and Wave optics.
615 24$aDifferential Equations.
676   $a519.6
700   $aGutiérrez$b Cristian E$066032
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910770271403321
996   $aOptimal Transport and Applications to Geometric Optics$93660704
997   $aUNINA