Topics in optimal transportation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2003
|
| Schriftenreihe: | Graduate studies in mathematics
58 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke, Includes bibliographical references (S. 349 - 362) and index |
| Beschreibung: | XVI, 370 Seiten Ill. |
| ISBN: | 082183312X 9780821833124 |
Internformat
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| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2003 | |
| 300 | |a XVI, 370 Seiten |b Ill. | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 58 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke, Includes bibliographical references (S. 349 - 362) and index | ||
| 650 | 7 | |a Calculo de variações |2 larpcal | |
| 650 | 7 | |a Equações diferenciais ordinárias (textos avançados) |2 larpcal | |
| 650 | 4 | |a Monge-Ampère, Équations de | |
| 650 | 4 | |a Problèmes de transport (Programmation) | |
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| 650 | 7 | |a Teoria ergodica |2 larpcal | |
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Datensatz im Suchindex
| _version_ | 1804129803277697024 |
|---|---|
| adam_text | Contents
Preface ix
Notation xiii
Introduction 1
1. Formulation of the optimal transportation problem 1
2. Basic questions 6
3. Overview of the course 10
Chapter 1. The Kantorovich Duality 17
1.1. General duality 17
1.2. Distance cost functions 34
1.3. Appendix: A duality argument in Cb(X x Y) 39
1.4. Appendix: {0, l} valued costs and Strassen s theorem 44
Chapter 2. Geometry of Optimal Transportation 47
2.1. A duality based proof for the quadratic cost 48
2.2. The real line 73
2.3. Alternative arguments 78
2.4. Generalizations to other costs 85
2.5. More on c concave functions 103
Chapter 3. Brenier s Polar Factorization Theorem 107
3.1. Rearrangements and polar factorization 107
3.2. Historical motivations: fluid mechanics 111
3.3. Proof of Brenier s polar factorization theorem 119
v
vi Contents
3.4. Related facts 122
Chapter 4. The Monge Ampere Equation 125
4.1. Informal presentation 125
4.2. Regularity 131
4.3. Open problems 141
Chapter 5. Displacement Interpolation and Displacement
Convexity 143
5.1. Displacement interpolation 143
5.2. Displacement convexity 150
5.3. Application: uniqueness of ground state 163
5.4. The Eulerian point of view 165
Chapter 6. Geometric and Gaussian Inequalities 183
6.1. Brunn Minkowski and Prekopa Leindler inequalities 184
6.2. The Alesker Dar Milman diffeomorphism 190
6.3. Gaussian inequalities 192
6.4. Sobolev inequalities 200
Chapter 7. The Metric Side of Optimal Transportation 205
7.1. Monge Kantorovich distances 207
7.2. Topological properties 212
7.3. The real line 218
7.4. Behavior under rescaled convolution 220
7.5. An application to the Boltzmann equation 223
7.6. Linearization 233
Chapter 8. A Differential Point of View on Optimal
Transportation 237
8.1. A differential formulation of optimal transportation 238
8.2. Differential calculus 250
8.3. Monge Kantorovich induced dynamics 251
8.4. Time discretization 256
8.5. Differentiability of the quadratic Wasserstein distance 262
8.6. Non quadratic costs 266
Chapter 9. Entropy Production and Transportation
Inequalities 267
9.1. More on optimal transportation induced dissipative equations 268
Contents vii
9.2. Logarithmic Sobolev inequalities 279
9.3. Talagrand inequalities 291
9.4. HWI inequalities 297
9.5. Nonlinear generalizations: internal energy 301
9.6. Nonlinear generalizations: interaction energy 304
Chapter 10. Problems 307
List of Problems 308
Bibliography 349
Table of Short Statements 363
Index 367
|
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| institution | BVB |
| isbn | 082183312X 9780821833124 |
| language | English |
| lccn | 2003040350 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010185636 |
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| series | Graduate studies in mathematics |
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| spelling | Villani, Cédric 1973- (DE-588)13389701X aut Topics in optimal transportation Cédric Villani Providence, RI American Mathematical Society 2003 XVI, 370 Seiten Ill. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 58 Hier auch später erschienene, unveränderte Nachdrucke, Includes bibliographical references (S. 349 - 362) and index Calculo de variações larpcal Equações diferenciais ordinárias (textos avançados) larpcal Monge-Ampère, Équations de Problèmes de transport (Programmation) Programação matemática larpcal Teoria ergodica larpcal Monge-Ampère equations Transportation problems (Programming) Transportproblem (DE-588)4060694-6 gnd rswk-swf Transportproblem (DE-588)4060694-6 s DE-604 Graduate studies in mathematics 58 (DE-604)BV009739289 58 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010185636&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Villani, Cédric 1973- Topics in optimal transportation Graduate studies in mathematics Calculo de variações larpcal Equações diferenciais ordinárias (textos avançados) larpcal Monge-Ampère, Équations de Problèmes de transport (Programmation) Programação matemática larpcal Teoria ergodica larpcal Monge-Ampère equations Transportation problems (Programming) Transportproblem (DE-588)4060694-6 gnd |
| subject_GND | (DE-588)4060694-6 |
| title | Topics in optimal transportation |
| title_auth | Topics in optimal transportation |
| title_exact_search | Topics in optimal transportation |
| title_full | Topics in optimal transportation Cédric Villani |
| title_fullStr | Topics in optimal transportation Cédric Villani |
| title_full_unstemmed | Topics in optimal transportation Cédric Villani |
| title_short | Topics in optimal transportation |
| title_sort | topics in optimal transportation |
| topic | Calculo de variações larpcal Equações diferenciais ordinárias (textos avançados) larpcal Monge-Ampère, Équations de Problèmes de transport (Programmation) Programação matemática larpcal Teoria ergodica larpcal Monge-Ampère equations Transportation problems (Programming) Transportproblem (DE-588)4060694-6 gnd |
| topic_facet | Calculo de variações Equações diferenciais ordinárias (textos avançados) Monge-Ampère, Équations de Problèmes de transport (Programmation) Programação matemática Teoria ergodica Monge-Ampère equations Transportation problems (Programming) Transportproblem |
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