Optimal transportation and applications: lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2003
|
| Schriftenreihe: | Lecture notes in mathematics
1813 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 169 S. Ill., graph. Darst. |
| ISBN: | 354040192X |
Internformat
MARC
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| 245 | 1 | 0 | |a Optimal transportation and applications |b lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 |c L. Ambrosio ... ; eds.: L.A. Caffarelli ... |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS THE MONGE-AMP` ERE EQUATION AND OPTIMAL TRANSPORTATION, AN
ELEMENTARY REVIEW LUIS CAFFARELLI
................................................... 1 1 OPTIMAL
TRANSPORTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 1 2 THE CONTINUOUS CASE: . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 THE DUAL
PROBLEM: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 3 4 EXISTENCE AND UNIQUENESS: . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 THE
POTENTIAL EQUATION: . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 6 6 SOME REMARKS ON THE STRUCTURE OF THE
EQUATION . . . . . . . . . . . . . . . . . . . . 7 OPTIMAL SHAPES AND
MASSES, AND OPTIMAL TRANSPORTATION PROBLEMS GIUSEPPE BUTTAZZO, LUIGI DE
PASCALE ............................... 11 1 INTRODUCTION . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 11 2 SOME CLASSICAL PROBLEMS . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 THE
ISOPERIMETRIC PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 13 2.2 THE NEWTON*S PROBLEM OF OPTIMAL AERODYNAMICAL
PROFILES . . . . . . . 14 2.3 OPTIMAL DIRICHLET REGIONS. . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 OPTIMAL
MIXTURES OF TWO CONDUCTORS . . . . . . . . . . . . . . . . . . . . . . .
. . 19 3 MASS OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 23 4 OPTIMAL TRANSPORTATION PROBLEMS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.1
THE OPTIMAL MASS TRANSPORTATION PROBLEM: MONGE AND KANTOROVICH
FORMULATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 30 4.2 THE PDE FORMULATION OF THE MASS TRANSPORTATION PROBLEM
. . . . . . 32 5 RELATIONSHIPS BETWEEN OPTIMAL MASS AND OPTIMAL
TRANSPORTATION . . . . . 33 6 FURTHER RESULTS AND OPEN PROBLEMS . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 35 6.1 A VECTORIAL
EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 35 6.2 A P * LAPLACIAN APPROXIMATION . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 37 6.3 OPTIMIZATION OF DIRICHLET
REGIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.4
OPTIMAL TRANSPORTING DISTANCES. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 40 REFERENCES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
VIII CONTENTS OPTIMAL TRANSPORTATION, DISSIPATIVE PDE*S AND FUNCTIONAL
INEQUALITIES CEDRIC VILLANI
................................................... 53 1 SOME
MOTIVATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 54 2 A STUDY OF FAST TREND TO EQUILIBRIUM
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3 A STUDY
OF SLOW TREND TO EQUILIBRIUM . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 64 4 ESTIMATES IN A MEAN-FIELD LIMIT PROBLEM . . . . . . .
. . . . . . . . . . . . . . . . . . . 71 5 OTTO*S DIFFERENTIAL POINT OF
VIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 88 EXTENDED
MONGE-KANTOROVICH THEORY YANN BRENIER
.................................................... 91 1 ABSTRACT . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 91 2 GENERALIZED GEODESICS AND THE
MONGE-KANTOROVICH THEORY. . . . . . . . . . . 91 2.1 GENERALIZED
GEODESICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 91 2.2 EXTENSION TO PROBABILITY MEASURES . . . . . . . . .
. . . . . . . . . . . . . . . . . . 94 2.3 A DECOMPOSITION RESULT. . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.4
RELATIVISTIC MKT . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 97 2.5 A RELATIVISTIC HEAT EQUATION . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.6 LAPLACE*S
EQUATION AND MOSER*S LEMMA REVISITED . . . . . . . . . . . . . . . 100 3
GENERALIZED HARMONIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 102 3.1 CLASSICAL HARMONIC FUNCTIONS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.2 OPEN
PROBLEMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 105 4 MULTIPHASIC MKT . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5
GENERALIZED EXTREMAL SURFACES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 111 5.1 MKT REVISITED AS A SUBSET OF
GENERALIZED SURFACE THEORY . . . . . . . . 113 5.2 DEGENERATE QUADRATIC
COST FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 113 6
GENERALIZED EXTREMAL SURFACES IN R 5 AND ELECTRODYNAMICS. . . . . . . .
. . . 114 6.1 RECOVERY OF THE MAXWELL EQUATIONS . . . . . . . . . . . .
. . . . . . . . . . . . . . 115 6.2 DERIVATION OF A SET OF NONLINEAR
MAXWELL EQUATIONS . . . . . . . . . . . . . 116 6.3 AN
EULER-MAXWELL-TYPE SYSTEM . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 118 REFERENCES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
EXISTENCE AND STABILITY RESULTS IN THE L 1 THEORY OF OPTIMAL
TRANSPORTATION LUIGI AMBROSIO, ALDO PRATELLI
...................................... 123 1 INTRODUCTION . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 123 2 NOTATION . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3
DUALITY AND OPTIMALITY CONDITIONS . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 130 4 * -CONVERGENCE AND * -ASYMPTOTIC
EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . 135 5
1-DIMENSIONAL THEORY . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 136 6 TRANSPORT RAYS AND TRANSPORT SET
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7 A
STABILITY RESULT . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 146 8 A COUNTEREXAMPLE . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 150 9 APPENDIX: DISINTEGRATION OF MEASURES . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 152 REFERENCES . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 158
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| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV017252986 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:15:44Z |
| institution | BVB |
| isbn | 354040192X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010399353 |
| oclc_num | 52424026 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-521 DE-634 DE-83 DE-188 DE-706 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-521 DE-634 DE-83 DE-188 DE-706 |
| physical | VIII, 169 S. Ill., graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 L. Ambrosio ... ; eds.: L.A. Caffarelli ... Berlin [u.a.] Springer 2003 VIII, 169 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1813 Análise matemática (congressos) larpcal Equações diferenciais parciais eliticas (congressos) larpcal Optimaliseren gtt Optimisation mathématique - Congrès Problemas variacionais (congressos) larpcal Problèmes de transport (Programmation) - Congrès Programação matemática (congressos) larpcal Sistemas de transportes (congressos) larpcal Teoria de sistemas e controle (congressos) larpcal Transportvergelijkingen gtt Transportation problems -- Congresses Mathematical optimization -- Congresses Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd rswk-swf Transportproblem (DE-588)4060694-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2001 Martina Franca gnd-content Transportproblem (DE-588)4060694-6 s Monge-Ampère-Differentialgleichung (DE-588)4253327-2 s DE-604 Ambrosio, Luigi 1963- Sonstige (DE-588)133791408 oth Caffarelli, Luis A. Sonstige oth Lecture notes in mathematics 1813 (DE-604)BV000676446 1813 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010399353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 Lecture notes in mathematics Análise matemática (congressos) larpcal Equações diferenciais parciais eliticas (congressos) larpcal Optimaliseren gtt Optimisation mathématique - Congrès Problemas variacionais (congressos) larpcal Problèmes de transport (Programmation) - Congrès Programação matemática (congressos) larpcal Sistemas de transportes (congressos) larpcal Teoria de sistemas e controle (congressos) larpcal Transportvergelijkingen gtt Transportation problems -- Congresses Mathematical optimization -- Congresses Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd Transportproblem (DE-588)4060694-6 gnd |
| subject_GND | (DE-588)4253327-2 (DE-588)4060694-6 (DE-588)1071861417 |
| title | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 |
| title_auth | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 |
| title_exact_search | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 |
| title_full | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 L. Ambrosio ... ; eds.: L.A. Caffarelli ... |
| title_fullStr | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 L. Ambrosio ... ; eds.: L.A. Caffarelli ... |
| title_full_unstemmed | Optimal transportation and applications lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 L. Ambrosio ... ; eds.: L.A. Caffarelli ... |
| title_short | Optimal transportation and applications |
| title_sort | optimal transportation and applications lectures given at the c i m e summer school held in martina franca italy september 2 8 2001 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2 - 8, 2001 |
| topic | Análise matemática (congressos) larpcal Equações diferenciais parciais eliticas (congressos) larpcal Optimaliseren gtt Optimisation mathématique - Congrès Problemas variacionais (congressos) larpcal Problèmes de transport (Programmation) - Congrès Programação matemática (congressos) larpcal Sistemas de transportes (congressos) larpcal Teoria de sistemas e controle (congressos) larpcal Transportvergelijkingen gtt Transportation problems -- Congresses Mathematical optimization -- Congresses Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd Transportproblem (DE-588)4060694-6 gnd |
| topic_facet | Análise matemática (congressos) Equações diferenciais parciais eliticas (congressos) Optimaliseren Optimisation mathématique - Congrès Problemas variacionais (congressos) Problèmes de transport (Programmation) - Congrès Programação matemática (congressos) Sistemas de transportes (congressos) Teoria de sistemas e controle (congressos) Transportvergelijkingen Transportation problems -- Congresses Mathematical optimization -- Congresses Monge-Ampère-Differentialgleichung Transportproblem Konferenzschrift 2001 Martina Franca |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010399353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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