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010   $a3-030-72162-0
024 7 $a10.1007/978-3-030-72162-6
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035   $a(OCoLC)1261380181
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035   $a(DE-He213)978-3-030-72162-6
035   $a(EXLCZ)994100000011984432
100   $a20210722d2021      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aLectures on Optimal Transport /$fby Luigi Ambrosio, Elia Brué, Daniele Semola
205   $a1st ed. 2021.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021.
215   $a1 online resource (250 pages)
225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v130
311 08$a3-030-72161-2 
320   $aIncludes bibliographical references.
327   $a1 Lecture 1: Preliminary notions and the Monge problem -- 2 Lecture 2: The Kantorovich problem -- 3 Lecture 3: The Kantorovich - Rubinstein duality -- 4 Lecture 4: Necessary and sufficient optimality conditions -- 5 Lecture 5: Existence of optimal maps and applications -- 6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport -- 7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds -- 8 Lecture 8: The metric side of Optimal Transport -- 9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport -- 10 Lecture 10: Wasserstein geodesics, nonbranching and curvature -- 11 Lecture 11: Gradient flows: an introduction -- 12 Lecture 12: Gradient flows: the Brézis-Komura theorem -- 13 Lecture 13: Examples of gradient flows in PDEs -- 14 Lecture 14: Gradient flows: the EDE and EDI formulations -- 15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space -- 16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup -- 17 Lecture 17: The Benamou-Brenier formula -- 18 Lecture 18: An introduction to Otto?s calculus -- 19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature.
330   $aThis textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
410  0$aLa Matematica per il 3+2,$x2038-5757 ;$v130
606   $aMathematical analysis
606   $aMathematical optimization
606   $aCalculus of variations
606   $aMeasure theory
606   $aAnalysis
606   $aCalculus of Variations and Optimization
606   $aMeasure and Integration
615  0$aMathematical analysis.
615  0$aMathematical optimization.
615  0$aCalculus of variations.
615  0$aMeasure theory.
615 14$aAnalysis.
615 24$aCalculus of Variations and Optimization.
615 24$aMeasure and Integration.
676   $a519.6
700   $aAmbrosio$b Luigi$044009
702   $aBrue?$b Elia
702   $aSemola$b Daniele
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910495195503321
996   $aLectures on Optimal Transport$92175022
997   $aUNINA