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001438437 001__ 1438437
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001438437 020__ $$a9783030721626$$q(electronic bk.)
001438437 020__ $$a3030721620$$q(electronic bk.)
001438437 020__ $$z3030721612
001438437 020__ $$z9783030721619
001438437 0247_ $$a10.1007/978-3-030-72162-6$$2doi
001438437 035__ $$aSP(OCoLC)1261380181
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001438437 08204 $$a519.6$$223
001438437 1001_ $$aAmbrosio, Luigi,$$eauthor.
001438437 24510 $$aLectures on optimal transport /$$cLuigi Ambrosio, Elia Brué, Daniele Semola.
001438437 260__ $$aCham, Switzerland :$$bSpringer,$$c2021.
001438437 300__ $$a1 online resource
001438437 336__ $$atext$$btxt$$2rdacontent
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001438437 4901_ $$aUnitext,$$x2038-5722 ;$$vv. 130
001438437 504__ $$aIncludes bibliographical references.
001438437 5050_ $$a1 Lecture 1: Preliminary notions and the Monge problem -- 2 Lecture 2: The Kantorovich problem -- 3 Lecture 3: The Kantorovich - Rubinstein duality -- 4 Lecture 4: Necessary and sufficient optimality conditions -- 5 Lecture 5: Existence of optimal maps and applications -- 6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport -- 7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds -- 8 Lecture 8: The metric side of Optimal Transport -- 9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport -- 10 Lecture 10: Wasserstein geodesics, nonbranching and curvature -- 11 Lecture 11: Gradient flows: an introduction -- 12 Lecture 12: Gradient flows: the Brézis-Komura theorem -- 13 Lecture 13: Examples of gradient flows in PDEs -- 14 Lecture 14: Gradient flows: the EDE and EDI formulations -- 15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space -- 16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup -- 17 Lecture 17: The Benamou-Brenier formula -- 18 Lecture 18: An introduction to Otto's calculus -- 19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature.
001438437 506__ $$aAccess limited to authorized users.
001438437 520__ $$aThis textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
001438437 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 30, 2021).
001438437 650_0 $$aMathematical optimization.
001438437 650_6 $$aOptimisation mathématique.
001438437 655_0 $$aElectronic books.
001438437 7001_ $$aBrué, Elia,$$eauthor.
001438437 7001_ $$aSemola, Daniele,$$eauthor.
001438437 77608 $$iPrint version:$$aAmbrosio, Luigi.$$tLectures on optimal transport.$$dCham, Switzerland : Springer, 2021$$z3030721612$$z9783030721619$$w(OCoLC)1240306003
001438437 830_0 $$aUnitext ;$$v130.$$x2038-5722
001438437 852__ $$bebk
001438437 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-72162-6$$zOnline Access$$91397441.1
001438437 909CO $$ooai:library.usi.edu:1438437$$pGLOBAL_SET
001438437 980__ $$aBIB
001438437 980__ $$aEBOOK
001438437 982__ $$aEbook
001438437 983__ $$aOnline
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