Optimal transportation and action-minimizing measures:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Pisa
Ed. della Normale
2008
|
| Schriftenreihe: | Tesi
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 254 S. |
| ISBN: | 9788876423307 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035031767 | ||
| 003 | DE-604 | ||
| 005 | 20150528 | ||
| 007 | t | ||
| 008 | 080901s2008 m||| 00||| eng d | ||
| 020 | |a 9788876423307 |9 978-88-7642-330-7 | ||
| 035 | |a (OCoLC)494080346 | ||
| 035 | |a (DE-599)BVBBV035031767 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-355 |a DE-188 | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 880 |0 (DE-625)143266: |2 rvk | ||
| 100 | 1 | |a Figalli, Alessio |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Optimal transportation and action-minimizing measures |c Alessio Figalli |
| 264 | 1 | |a Pisa |b Ed. della Normale |c 2008 | |
| 300 | |a XIX, 254 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Tesi |v 8 | |
| 502 | |a Zugl.: Diss. | ||
| 650 | 7 | |a Euler, Équations d' |2 ram | |
| 650 | 7 | |a Hamilton-Jacobi, Équations de |2 ram | |
| 650 | 7 | |a Transport optimal de mesure |2 ram | |
| 650 | 7 | |a Équations différentielles stochastiques |2 ram | |
| 650 | 0 | 7 | |a Transportproblem |0 (DE-588)4060694-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Strömungsmechanik |0 (DE-588)4077970-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Transportproblem |0 (DE-588)4060694-6 |D s |
| 689 | 0 | 1 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |D s |
| 689 | 0 | 2 | |a Strömungsmechanik |0 (DE-588)4077970-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Tesi |v 8 |w (DE-604)BV035447349 |9 8 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016700741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016700741 | ||
Datensatz im Suchindex
| _version_ | 1804137962541154304 |
|---|---|
| adam_text | Contents
Introduction
ix
1
The optimal transportation problem
1
1.1.
Introduction
........................ 1
1.2.
Background and some definitions
............. 3
1.3.
The main result
...................... 6
1.4.
Costs obtained from Lagrangians
............. 13
1.5.
The interpolation and its absolute continuity
....... 18
1.6.
The
Wasserstein
space W2
................ 25
1.6.1.
Regularity, concavity estimate and a displacement
convexity result
.................. 27
1.7.
Displacement convexity on Riemannian manifolds
... 33
1.7.1.
Proofs
....................... 38
1.8.
A generalization of the existence and uniqueness result
. 43
2
The irrigation problem
49
2.1.
Introduction
........................ 49
2.2.
Traffic plans
........................ 54
Stopping time, irrigated measures, transference plan
... 54
Energy of a traffic plan
.................. 55
Convergence
....................... 55
Existence of minimizers
................. 55
Stability with respect to
μ+
and
μ~
........... 56
Regularity
......................... 57
Extension of the time domain
............... 58
2.3.
Dynamic cost of a traffic plan
............... 58
2.4.
Synchronizable traffic plans
................ 62
2.5.
Equivalence of the dynamical and classical irrigation
problems
......................... 65
2.6.
Stability with respect to the cost
............. 66
vi
Alessio
Fîgaiîj
Variational
models for the incompressible
Euler
equations
71
3.1.
Introduction
........................ 71
3.2.
Notation and preliminary results
............. 78
3.3.
Variational models for generalized geodesies
....... 82
3.3.1.
Arnold s least action problem
.......... 82
3.3.2.
Brenier s Lagrangian model and its extensions
. 83
3.3.3.
Brenier s Eulerian-Lagrangian model
...... 89
3.4.
Equivalence of the two relaxed models
.......... 91
3.5.
Comparison of metrics and gap phenomena
....... 92
3.6.
Necessary and sufficient optimality conditions
...... 102
3.7.
Regularity of the pressure field
.............. 118
3.7.1.
A difference quotients estimate
......... 120
3.7.2.
Proof of the main result
.............. 123
On the structure of the Aubry set and Hamilton-Jacobi
equation
131
4.1.
Introduction
........................ 131
4.2.
Preparatory lemmas
.................... 136
4.3.
Existence of Cfo! critical
subsolution on
noncompact
manifolds
......................... 139
4.4.
Proofs of Theorems
4.1.1,4.1.2, 4.1.4.......... 144
4.4.1.
Proof of Theorem
4.1.1.............. 144
4.4.2.
Proof of Theorem
4.1.2.............. 146
4.4.3.
Proof of Theorem
4.1.4.............. 147
4.4.4.
A general result
.................. 152
4.5.
Proof of Theorem
4.1.5.................. 153
4.6.
Applications in Dynamics
................. 154
4.6.1.
Preliminary results
................ 154
4.6.2.
Strong Mather condition
............. 158
4.6.3.
Mané
Lagrangians
................ 161
»
DiPerna-Lions theory for SDE
165
5.1.
Introduction and preliminary results
........... 165
5.1.1.
Plan of the chapter
................ 168
5.2.
SDE-PDE uniqueness
................... 170
5.2.1.
A representation formula for solutions of the PDE
173
5.3.
Stochastic Lagrangian Flows
............... 178
5.3.1.
Existence, uniqueness and stability of SLF
. . . 179
5.3.2.
SLFversusRLF
................. 184
5.4.
Fokker-Planck equation
.................. 186
5.4.1.
Existence and uniqueness of measure valued so¬
lutions
.......... .... 186
vii
Optimal
Transportation
and Action-Minimizing Measures
5.4.2.
Existence and uniqueness of absolutely
continuous solutions in the uniformly parabolic
case
........................ 188
5.4.3.
Existence and uniqueness in the degenerate
parabolic case
................... 200
5.5.
Conclusions
........................ 206
5.6.
A generalized uniqueness result for martingale solutions
208
A
213
A.I. Semi-concave functions
.................. 213
A.2. Tonelli Lagrangians
.................... 223
A.2.1. Definition and background
............ 223
A.2.2. Lagrangian costs and semi-concavity
...... 235
A.2.3. The twist condition for costs obtained
from Lagrangians
................. 239
Bibliography
242
References
243
|
| adam_txt |
Contents
Introduction
ix
1
The optimal transportation problem
1
1.1.
Introduction
. 1
1.2.
Background and some definitions
. 3
1.3.
The main result
. 6
1.4.
Costs obtained from Lagrangians
. 13
1.5.
The interpolation and its absolute continuity
. 18
1.6.
The
Wasserstein
space W2
. 25
1.6.1.
Regularity, concavity estimate and a displacement
convexity result
. 27
1.7.
Displacement convexity on Riemannian manifolds
. 33
1.7.1.
Proofs
. 38
1.8.
A generalization of the existence and uniqueness result
. 43
2
The irrigation problem
49
2.1.
Introduction
. 49
2.2.
Traffic plans
. 54
Stopping time, irrigated measures, transference plan
. 54
Energy of a traffic plan
. 55
Convergence
. 55
Existence of minimizers
. 55
Stability with respect to
μ+
and
μ~
. 56
Regularity
. 57
Extension of the time domain
. 58
2.3.
Dynamic cost of a traffic plan
. 58
2.4.
Synchronizable traffic plans
. 62
2.5.
Equivalence of the dynamical and classical irrigation
problems
. 65
2.6.
Stability with respect to the cost
. 66
vi
Alessio
Fîgaiîj
Variational
models for the incompressible
Euler
equations
71
3.1.
Introduction
. 71
3.2.
Notation and preliminary results
. 78
3.3.
Variational models for generalized geodesies
. 82
3.3.1.
Arnold's least action problem
. 82
3.3.2.
Brenier's Lagrangian model and its extensions
. 83
3.3.3.
Brenier's Eulerian-Lagrangian model
. 89
3.4.
Equivalence of the two relaxed models
. 91
3.5.
Comparison of metrics and gap phenomena
. 92
3.6.
Necessary and sufficient optimality conditions
. 102
3.7.
Regularity of the pressure field
. 118
3.7.1.
A difference quotients estimate
. 120
3.7.2.
Proof of the main result
. 123
On the structure of the Aubry set and Hamilton-Jacobi
equation
131
4.1.
Introduction
. 131
4.2.
Preparatory lemmas
. 136
4.3.
Existence of Cfo! critical
subsolution on
noncompact
manifolds
. 139
4.4.
Proofs of Theorems
4.1.1,4.1.2, 4.1.4. 144
4.4.1.
Proof of Theorem
4.1.1. 144
4.4.2.
Proof of Theorem
4.1.2. 146
4.4.3.
Proof of Theorem
4.1.4. 147
4.4.4.
A general result
. 152
4.5.
Proof of Theorem
4.1.5. 153
4.6.
Applications in Dynamics
. 154
4.6.1.
Preliminary results
. 154
4.6.2.
Strong Mather condition
. 158
4.6.3.
Mané
Lagrangians
. 161
»
DiPerna-Lions theory for SDE
165
5.1.
Introduction and preliminary results
. 165
5.1.1.
Plan of the chapter
. 168
5.2.
SDE-PDE uniqueness
. 170
5.2.1.
A representation formula for solutions of the PDE
173
5.3.
Stochastic Lagrangian Flows
. 178
5.3.1.
Existence, uniqueness and stability of SLF
. . . 179
5.3.2.
SLFversusRLF
. 184
5.4.
Fokker-Planck equation
. 186
5.4.1.
Existence and uniqueness of measure valued so¬
lutions
. . 186
vii
Optimal
Transportation
and Action-Minimizing Measures
5.4.2.
Existence and uniqueness of absolutely
continuous solutions in the uniformly parabolic
case
. 188
5.4.3.
Existence and uniqueness in the degenerate
parabolic case
. 200
5.5.
Conclusions
. 206
5.6.
A generalized uniqueness result for martingale solutions
208
A
213
A.I. Semi-concave functions
. 213
A.2. Tonelli Lagrangians
. 223
A.2.1. Definition and background
. 223
A.2.2. Lagrangian costs and semi-concavity
. 235
A.2.3. The twist condition for costs obtained
from Lagrangians
. 239
Bibliography
242
References
243 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Figalli, Alessio |
| author_facet | Figalli, Alessio |
| author_role | aut |
| author_sort | Figalli, Alessio |
| author_variant | a f af |
| building | Verbundindex |
| bvnumber | BV035031767 |
| classification_rvk | SK 540 SK 880 |
| ctrlnum | (OCoLC)494080346 (DE-599)BVBBV035031767 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01849nam a2200469 cb4500</leader><controlfield tag="001">BV035031767</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150528 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080901s2008 m||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9788876423307</subfield><subfield code="9">978-88-7642-330-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)494080346</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035031767</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</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="100" ind1="1" ind2=" "><subfield code="a">Figalli, Alessio</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Optimal transportation and action-minimizing measures</subfield><subfield code="c">Alessio Figalli</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Pisa</subfield><subfield code="b">Ed. della Normale</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 254 S.</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">Tesi</subfield><subfield code="v">8</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Diss.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Euler, Équations d'</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Hamilton-Jacobi, Équations de</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Transport optimal de mesure</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Équations différentielles stochastiques</subfield><subfield code="2">ram</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="650" ind1="0" ind2="7"><subfield code="a">Strömungsmechanik</subfield><subfield code="0">(DE-588)4077970-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</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="1"><subfield code="a">Optimale Kontrolle</subfield><subfield code="0">(DE-588)4121428-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Strömungsmechanik</subfield><subfield code="0">(DE-588)4077970-1</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">Tesi</subfield><subfield code="v">8</subfield><subfield code="w">(DE-604)BV035447349</subfield><subfield code="9">8</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</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=016700741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016700741</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV035031767 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:50:06Z |
| indexdate | 2024-07-09T21:20:38Z |
| institution | BVB |
| isbn | 9788876423307 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016700741 |
| oclc_num | 494080346 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-188 |
| physical | XIX, 254 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Ed. della Normale |
| record_format | marc |
| series | Tesi |
| series2 | Tesi |
| spelling | Figalli, Alessio Verfasser aut Optimal transportation and action-minimizing measures Alessio Figalli Pisa Ed. della Normale 2008 XIX, 254 S. txt rdacontent n rdamedia nc rdacarrier Tesi 8 Zugl.: Diss. Euler, Équations d' ram Hamilton-Jacobi, Équations de ram Transport optimal de mesure ram Équations différentielles stochastiques ram Transportproblem (DE-588)4060694-6 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Transportproblem (DE-588)4060694-6 s Optimale Kontrolle (DE-588)4121428-6 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Tesi 8 (DE-604)BV035447349 8 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016700741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Figalli, Alessio Optimal transportation and action-minimizing measures Tesi Euler, Équations d' ram Hamilton-Jacobi, Équations de ram Transport optimal de mesure ram Équations différentielles stochastiques ram Transportproblem (DE-588)4060694-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4060694-6 (DE-588)4077970-1 (DE-588)4121428-6 (DE-588)4113937-9 |
| title | Optimal transportation and action-minimizing measures |
| title_auth | Optimal transportation and action-minimizing measures |
| title_exact_search | Optimal transportation and action-minimizing measures |
| title_exact_search_txtP | Optimal transportation and action-minimizing measures |
| title_full | Optimal transportation and action-minimizing measures Alessio Figalli |
| title_fullStr | Optimal transportation and action-minimizing measures Alessio Figalli |
| title_full_unstemmed | Optimal transportation and action-minimizing measures Alessio Figalli |
| title_short | Optimal transportation and action-minimizing measures |
| title_sort | optimal transportation and action minimizing measures |
| topic | Euler, Équations d' ram Hamilton-Jacobi, Équations de ram Transport optimal de mesure ram Équations différentielles stochastiques ram Transportproblem (DE-588)4060694-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Euler, Équations d' Hamilton-Jacobi, Équations de Transport optimal de mesure Équations différentielles stochastiques Transportproblem Strömungsmechanik Optimale Kontrolle Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016700741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035447349 |
| work_keys_str_mv | AT figallialessio optimaltransportationandactionminimizingmeasures |