Lectures on Optimal Transport (Record no. 66173)
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| fixed length control field | 04523nam a22005895i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-76834-7 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030114649.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031768347 |
| -- | 978-3-031-76834-7 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-76834-7 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA299.6-433 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBK |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT034000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBK |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Ambrosio, Luigi. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 77272 |
| 245 10 - TITLE STATEMENT | |
| Title | Lectures on Optimal Transport |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | by Luigi Ambrosio, Elia Brué, Daniele Semola. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XI, 260 p. 2 illus., 1 illus. in color. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | La Matematica per il 3+2, |
| International Standard Serial Number | 2038-5757 ; |
| Volume/sequential designation | 169 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | - 1. Lecture I. Preliminary notions and the Monge problem -- 2. Lecture II. The Kantorovich problem -- 3. Lecture III. The Kantorovich - Rubinstein duality -- 4. Lecture IV. Necessary and sufficient optimality conditions -- 5. Lecture V. Existence of optimal maps and applications -- 6. Lecture VI. A proof of the isoperimetric inequality and stability in Optimal Transport -- 7. Lecture VII. The Monge-Ampére equation and Optimal Transport on Riemannian manifolds -- 8. Lecture VIII. The metric side of Optimal Transport -- 9. Lecture IX. Analysis on metric spaces and the dynamic formulation of Optimal Transport -- 10. Lecture X.Wasserstein geodesics, nonbranching and curvature -- 11. Lecture XI. Gradient flows: an introduction -- 12. Lecture XII. Gradient flows: the Brézis-Komura theorem -- 13. Lecture XIII. Examples of gradient flows in PDEs -- 14. Lecture XIV. Gradient flows: the EDE and EDI formulations -- 15. Lecture XV. Semicontinuity and convexity of energies in the Wasserstein space -- 16. Lecture XVI. The Continuity Equation and the Hopf-Lax semigroup -- 17. Lecture XVII. The Benamou-Brenier formula -- 18. Lecture XVIII. An introduction to Otto’s calculus -- 19. Lecture XIX. Heat flow, Optimal Transport and Ricci curvature. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This 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. This is the second edition of the book, first published in 2018. It includes refinement of proofs, an updated bibliography and a more detailed discussion of minmax principles, with the aim of giving two fully self-contained proofs of Kantorovich duality. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 64178 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
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| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 9 (RLIN) | 67270 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
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| 9 (RLIN) | 71219 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 65523 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Brué, Elia. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 89828 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Semola, Daniele. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 89829 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031768330 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031768354 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | La Matematica per il 3+2, |
| International Standard Serial Number | 2038-5757 ; |
| Volume number/sequential designation | 169 |
| 9 (RLIN) | 70145 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-76834-7">https://doi.org/10.1007/978-3-031-76834-7</a> |
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