Variational problems in transport theory with mass concentration:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Pisa
Ed. della Normale
2007
|
| Schriftenreihe: | Tesi / Scuola Normale Superiore Pisa
4 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016741054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Zugl.: Pisa, Scuola Normale Superiore, Diss., 2006 |
| Umfang: | XXXII, 198 S. graph. Darst. |
| ISBN: | 9788876423123 |
Internformat
MARC
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| 100 | 1 | |a Santambrogio, Filippo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Variational problems in transport theory with mass concentration |c Filippo Santambrogio |
| 264 | 1 | |a Pisa |b Ed. della Normale |c 2007 | |
| 300 | |a XXXII, 198 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Tesi / Scuola Normale Superiore Pisa |v 4 | |
| 500 | |a Zugl.: Pisa, Scuola Normale Superiore, Diss., 2006 | ||
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Transport theory | |
| 650 | 4 | |a Transportation problems (Programming) | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016741054 | |
Datensatz im Suchindex
| _version_ | 1819339112026472448 |
|---|---|
| adam_text | Contents
Introduction
ix
Acknowledgments
xxix
Notations
xxxi
Preliminaries on optimal transportation
1
0.1.
Primal and dual problems
................. 1
0.2. Wasserstein
distances and spaces
............. 6
0.3.
Geodesies, continuity equation and displacement convexity
7
0.4.
Monge-Ampère
equation and regularity
......... 10
1
An urban planning model by local functionals
13
1.1. Overall optimization of residence and working areas
. .
ІЗ
1.2.
Local semicontinuous functionals on measures
..... 15
1.3.
Interpretation of the model
................ 16
1
.4.
Necessary optimality conditions on
$,.......... 18
1
.4.
1
.
An approximation proof
............. 19
1.4.2.
A convex analysis proof
............. 26
1.5.
Whole minimization on bounded and unbounded domains
30
1.6.
Comments on the model and its results
.......... 37
2
An urban planning model with traffic congestion
39
2.1.
Traffic congestion
..................... 40
2.2.
The minimization problem
................ 42
2.3.
Minimization with respect to
μ.
.............. 43
2.4.
Optimality conditions
................... 45
2.5.
Regularity via approximation
............... 48
2.5.1.
L^ estimates in the convex case
......... 50
2.5.2.
Interior L2 estimates in the general case
..... 53
vi Filippo Santambrogio
2.6.
Qualitative
properties of the minimizers
......... 55
2.7.
Geodesie
convexity in dimension one
.......... 57
2.8.
The quadratic case in two dimensions
.......... 59
3
Transport and concentration problems with interaction
65
3.1.
Variational problems for transport and concentration
. . 65
3.2.
Optimality conditions for the interaction case
...... 68
3.3.
An explicit example
.................... 73
4
Path
funcţionale
in
Wasserstein
spaces
79
4.1.
The metric framework
.................. 79
4.2.
The case of the space of probability measures
...... 82
4.2.1.
Concentration
................... 84
4.2.2.
Diffusion
..................... 89
4.3.
The non-compact case
.................. 92
5
A system of PDEs from a geodesic problem in Wp
97
5.1.
Compressible
Euler
equations from geodesic problems
. 97
5.2.
Optimality conditions for weighted
Wasserstein
geodesies
99
5.2.1.
A new velocity vector field
............ 99
5.2.2.
Derivation of the optimality conditions
..... 101
5.2.3.
The resulting system of PDEs
.......... 106
5.3.
Self-similar solutions
................... 108
5.3.1.
Homothetic solutions with fixed center
.....
Ю8
5.3.2.
Moving self-similar solutions
..........
Ш
6
Branching transport problems and distances
115
6.1.
Eulerian models by Gilbert and Xia
........... 115
6.2.
Lagrangian models: traffic plans and patterns
......
Π
7
6.3.
Irrigation costs and their flniteness
............ 121
6.4.
The da distance and its comparison with
W
χ.......
123
7
Landscape function
129
7.1.
Motivations
........................ 129
7.1.1.
Landscape equilibrium and OCNs in geophysics
129
7.1.2.
A landscape function appearing for derivative pur¬
poses
....................... 132
7.2.
A general development formula
............. 135
7.3.
Landscape function: existence and applications
..... 136
7.3.1.
Well-definedness of the landscape function
... 136
7.3.2.
Variational applications: the functional Xa
... 139
7.3.3.
A transport and concentration problem
...... 141
Variational
Problems in Transport
Theory with Mass Concentration
7.4.
Properties of the landscape function
........... 142
7.4.1.
Semicontinuity
.................. 142
7.4.2.
Maximal slope in the network direction
..... 143
7.5.
Holder continuity under extra assumptions
........ 145
7.5.1.
Campanaio
spaces by medians
.......... 146
7.5.2.
Holder continuity of the landscape function
. . . 147
8
Blow-up for optimal one-dimensional sets
151
8.1.
Average distance problems and free Dirichlet regions
. . 151
8.2.
Preliminary and auxiliary results
............. 153
8.2.1.
The function
θ
and its variation
......... 158
8.2.2.
Blow-up limits, up to subsequences
....... 162
8.2.3.
r-Convergence
................. 164
8.2.4.
Iterated estimates for small diameters
...... 167
8.3.
Blow-up limits
...................... 169
8.3.1.
Triple junctions
.................. 169
8.3.2. Endpoints..................... 170
8.3.3.
Ordinary points
.................. 171
8.4.
Something more on regularity
.............. 175
9
Blow-up for optimal branching structures
179
9.1.
Techical tools
....................... 179
9.1.1.
Geometric estimates
............... 179
9.1.2.
Concatenation of traffic plans
.......... 181
9.2.
Blow-up at branching points
............... 183
References
191
|
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV035072676 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:19:29Z |
| institution | BVB |
| isbn | 9788876423123 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016741054 |
| oclc_num | 181090569 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 |
| physical | XXXII, 198 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Ed. della Normale |
| record_format | marc |
| series2 | Tesi / Scuola Normale Superiore Pisa |
| spellingShingle | Santambrogio, Filippo Variational problems in transport theory with mass concentration Calculus of variations Transport theory Transportation problems (Programming) Variationsrechnung (DE-588)4062355-5 gnd Transporttheorie (DE-588)4185936-4 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4185936-4 (DE-588)4113937-9 |
| title | Variational problems in transport theory with mass concentration |
| title_auth | Variational problems in transport theory with mass concentration |
| title_exact_search | Variational problems in transport theory with mass concentration |
| title_full | Variational problems in transport theory with mass concentration Filippo Santambrogio |
| title_fullStr | Variational problems in transport theory with mass concentration Filippo Santambrogio |
| title_full_unstemmed | Variational problems in transport theory with mass concentration Filippo Santambrogio |
| title_short | Variational problems in transport theory with mass concentration |
| title_sort | variational problems in transport theory with mass concentration |
| topic | Calculus of variations Transport theory Transportation problems (Programming) Variationsrechnung (DE-588)4062355-5 gnd Transporttheorie (DE-588)4185936-4 gnd |
| topic_facet | Calculus of variations Transport theory Transportation problems (Programming) Variationsrechnung Transporttheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016741054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022416811 |
| work_keys_str_mv | AT santambrogiofilippo variationalproblemsintransporttheorywithmassconcentration |