Topics in optimal transportation:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2003
|
| Schriftenreihe: | Graduate studies in mathematics
58 |
| Schlagwörter: | |
| Links: | 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 |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke, Includes bibliographical references (S. 349 - 362) and index |
| Umfang: | XVI, 370 Seiten Ill. |
| ISBN: | 082183312X 9780821833124 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV016475178 | ||
| 003 | DE-604 | ||
| 005 | 20200728 | ||
| 007 | t| | ||
| 008 | 030128s2003 xxua||| |||| 00||| eng d | ||
| 010 | |a 2003040350 | ||
| 020 | |a 082183312X |9 0-8218-3312-X | ||
| 020 | |a 9780821833124 |9 978-0-8218-3312-4 | ||
| 035 | |a (OCoLC)51477002 | ||
| 035 | |a (DE-599)BVBBV016475178 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-355 |a DE-703 |a DE-29T |a DE-19 |a DE-91G |a DE-634 |a DE-83 |a DE-11 |a DE-188 |a DE-384 |a DE-20 |a DE-706 | ||
| 050 | 0 | |a QA402.6 | |
| 082 | 0 | |a 519.72 | |
| 082 | 0 | |a 519.7/2 |2 21 | |
| 084 | |a SK 880 |0 (DE-625)143266: |2 rvk | ||
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 084 | |a 49N15 |2 msc | ||
| 084 | |a MAT 908f |2 stub | ||
| 084 | |a MAT 912f |2 stub | ||
| 084 | |a 90B06 |2 msc | ||
| 084 | |a 49J20 |2 msc | ||
| 084 | |a MAT 355f |2 stub | ||
| 084 | |a PHY 063f |2 stub | ||
| 100 | 1 | |a Villani, Cédric |d 1973- |0 (DE-588)13389701X |4 aut | |
| 245 | 1 | 0 | |a Topics in optimal transportation |c Cédric Villani |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2003 | |
| 300 | |a XVI, 370 Seiten |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 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) | |
| 650 | 7 | |a Programação matemática |2 larpcal | |
| 650 | 7 | |a Teoria ergodica |2 larpcal | |
| 650 | 4 | |a Monge-Ampère equations | |
| 650 | 4 | |a Transportation problems (Programming) | |
| 650 | 0 | 7 | |a Transportproblem |0 (DE-588)4060694-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Transportproblem |0 (DE-588)4060694-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate studies in mathematics |v 58 |w (DE-604)BV009739289 |9 58 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010185636 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 912f 2009 B 771 |
|---|---|
| DE-BY-TUM_katkey | 1678979 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010147903 |
| _version_ | 1821933606565576705 |
| 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
|
| any_adam_object | 1 |
| author | Villani, Cédric 1973- |
| author_GND | (DE-588)13389701X |
| author_facet | Villani, Cédric 1973- |
| author_role | aut |
| author_sort | Villani, Cédric 1973- |
| author_variant | c v cv |
| building | Verbundindex |
| bvnumber | BV016475178 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.6 |
| callnumber-search | QA402.6 |
| callnumber-sort | QA 3402.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 880 SK 890 SK 870 |
| classification_tum | MAT 908f MAT 912f MAT 355f PHY 063f |
| ctrlnum | (OCoLC)51477002 (DE-599)BVBBV016475178 |
| dewey-full | 519.72 519.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.72 519.7/2 |
| dewey-search | 519.72 519.7/2 |
| dewey-sort | 3519.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02404nam a2200625zcb4500</leader><controlfield tag="001">BV016475178</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200728 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">030128s2003 xxua||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2003040350</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">082183312X</subfield><subfield code="9">0-8218-3312-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821833124</subfield><subfield code="9">978-0-8218-3312-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)51477002</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV016475178</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA402.6</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.72</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.7/2</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 880</subfield><subfield code="0">(DE-625)143266:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 870</subfield><subfield code="0">(DE-625)143265:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">49N15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 908f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 912f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">90B06</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">49J20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 355f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 063f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Villani, Cédric</subfield><subfield code="d">1973-</subfield><subfield code="0">(DE-588)13389701X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Topics in optimal transportation</subfield><subfield code="c">Cédric Villani</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 370 Seiten</subfield><subfield code="b">Ill.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">58</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke, Includes bibliographical references (S. 349 - 362) and index</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Calculo de variações</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Equações diferenciais ordinárias (textos avançados)</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Monge-Ampère, Équations de</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Problèmes de transport (Programmation)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Programação matemática</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Teoria ergodica</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Monge-Ampère equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transportation problems (Programming)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Transportproblem</subfield><subfield code="0">(DE-588)4060694-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Transportproblem</subfield><subfield code="0">(DE-588)4060694-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">58</subfield><subfield code="w">(DE-604)BV009739289</subfield><subfield code="9">58</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010185636</subfield></datafield></record></collection> |
| id | DE-604.BV016475178 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:12:01Z |
| institution | BVB |
| isbn | 082183312X 9780821833124 |
| language | English |
| lccn | 2003040350 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010185636 |
| oclc_num | 51477002 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188 DE-384 DE-20 DE-706 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188 DE-384 DE-20 DE-706 |
| physical | XVI, 370 Seiten Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| 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 |
| url | 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 |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT villanicedric topicsinoptimaltransportation |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 912f 2009 B 771 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Ausgeliehen – Rückgabe bis: 25.03.2025 |