Variational methods in shape optimization problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2005
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
65 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 216 S. graph. Darst. |
| ISBN: | 0817643591 9780817643591 |
Internformat
MARC
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| 020 | |a 9780817643591 |9 978-0-8176-4359-1 | ||
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| 100 | 1 | |a Bucur, Dorin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Variational methods in shape optimization problems |c Dorin Bucur ; Giuseppe Buttazzo |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2005 | |
| 300 | |a VIII, 216 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 65 | |
| 650 | 4 | |a Formes | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Shapes | |
| 650 | 0 | 7 | |a Gestaltoptimierung |0 (DE-588)4329076-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Variationsrechnung |0 (DE-588)4062355-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gestaltoptimierung |0 (DE-588)4329076-0 |D s |
| 689 | 0 | 1 | |a Variationsrechnung |0 (DE-588)4062355-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Buttazzo, Giuseppe |d 1954- |e Verfasser |0 (DE-588)113360568 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 0-8176-4403-2 |
| 830 | 0 | |a Progress in nonlinear differential equations and their applications |v 65 |w (DE-604)BV007934389 |9 65 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-013522933 | ||
Datensatz im Suchindex
| _version_ | 1804133768981643264 |
|---|---|
| adam_text | Contents
Preface
Vil
1
Introduction
to Shape Optimization Theory and
Some Classical Problems
...................................... 1
1.1
General formulation of a shape optimization problem
............ 3
1.2
The isoperimetric problem and some of its variants
.............. 3
1.3
The Newton problem of minimal aerodynamical resistance
........ 11
1.4
Optimal interfaces between two media
......................... 18
1.5
The optimal shape of a thin insulating layer
..................... 22
2
Optimization Problems over Classes of Convex Domains
........... 31
2.1
A general existence result for variational integrals
............... 31
2.2
Some necessary conditions of optimality
....................... 37
2.3
Optimization for boundary integrals
........................... 43
2.4
Problems governed by PDE of higher order
..................... 48
3
Optimal Control Problems: A General Scheme
................... 53
3.1
A topological framework for general optimization problems
....... 54
3.2
A quick survey on
Γ
-convergence theory
....................... 56
3.3
The topology of
y
-convergence for control variables
............. 57
3.4
A general definition of relaxed controls
........................ 58
3.5
Optimal control problems governed by ODE
.................... 59
3.6
Examples of relaxed shape optimization problems
............... 70
4
Shape Optimization Problems with Dirichlet Condition
on the Free Boundary
......................................... 75
4.1
A short survey on capacities
.................................. 75
4.2
Nonexistence of optimal solutions
............................. 78
4.3
The relaxed form of a Dirichlet problem
....................... 80
4.4
Necessary conditions of optimality
............................ 88
4.5
Boundary variation
......................................... 94
vi
Contents
4.6
Continuity under geometric constraints
........................ 100
4.7
Continuity under topological constraints:
Šverák s
result
.......... 105
4.8
Nonlinear operators: Necessary and sufficient conditions for the
γ ρ
-convergence
............................................ 107
4.9
Stability in the sense of Keldysh
.............................. 117
4.10 Furtherremarks
and generalizations
........................... 118
5
Existence of Classical Solutions
.................................121
5.1
Existence of optimal domains under geometrical constraints
....... 121
5.2
A general abstract result for monotone costs
.................... 123
5.3
The weak
y
-convergence for quasi-open domains
................ 124
5.4
Examples of monotone costs
................................. 125
5.5
The problem of optimal partitions
............................. 127
5.6
Optimal obstacles
.......................................... 132
6
Optimization Problems for Functions of Eigenvalues
...............145
6.1
Stability of eigenvalues under geometric domain perturbation
...... 145
6.2
Setting the optimization problem
.............................. 149
6.3
A short survey on continuous
Steiner
symmetrization
............ 150
6.4
The case of the first two eigenvalues of the Laplace operator
...... 154
6.5
Unbounded design regions
................................... 160
6.6
Some open questions
....................................... 172
7
Shape Optimization Problems with Neumann Condition
on the Free Boundary
......................................... 175
7.1
Some examples
............................................ 176
7.2
Boundary variation for Neumann problems
..................... 180
7.2.1
General facts in R^
.................................. 181
7.2.2
Topological constraints for shape stability
................ 188
7.3
The optimal cutting problem
................................. 192
7.4
Eigenvalues of the Neumann Laplacian
........................ 196
Bibliography
....................................................205
Index
...........................................................215
|
| any_adam_object | 1 |
| author | Bucur, Dorin Buttazzo, Giuseppe 1954- |
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| classification_tum | MAT 492f |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV020817520 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:13:58Z |
| institution | BVB |
| isbn | 0817643591 9780817643591 |
| language | English |
| lccn | 2005045239 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013522933 |
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| physical | VIII, 216 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Bucur, Dorin Verfasser aut Variational methods in shape optimization problems Dorin Bucur ; Giuseppe Buttazzo Boston [u.a.] Birkhäuser 2005 VIII, 216 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 65 Formes Optimisation mathématique Mathematical optimization Shapes Gestaltoptimierung (DE-588)4329076-0 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Gestaltoptimierung (DE-588)4329076-0 s Variationsrechnung (DE-588)4062355-5 s DE-604 Buttazzo, Giuseppe 1954- Verfasser (DE-588)113360568 aut Erscheint auch als Online-Ausgabe 0-8176-4403-2 Progress in nonlinear differential equations and their applications 65 (DE-604)BV007934389 65 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013522933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bucur, Dorin Buttazzo, Giuseppe 1954- Variational methods in shape optimization problems Progress in nonlinear differential equations and their applications Formes Optimisation mathématique Mathematical optimization Shapes Gestaltoptimierung (DE-588)4329076-0 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4329076-0 (DE-588)4062355-5 |
| title | Variational methods in shape optimization problems |
| title_auth | Variational methods in shape optimization problems |
| title_exact_search | Variational methods in shape optimization problems |
| title_full | Variational methods in shape optimization problems Dorin Bucur ; Giuseppe Buttazzo |
| title_fullStr | Variational methods in shape optimization problems Dorin Bucur ; Giuseppe Buttazzo |
| title_full_unstemmed | Variational methods in shape optimization problems Dorin Bucur ; Giuseppe Buttazzo |
| title_short | Variational methods in shape optimization problems |
| title_sort | variational methods in shape optimization problems |
| topic | Formes Optimisation mathématique Mathematical optimization Shapes Gestaltoptimierung (DE-588)4329076-0 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Formes Optimisation mathématique Mathematical optimization Shapes Gestaltoptimierung Variationsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013522933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT bucurdorin variationalmethodsinshapeoptimizationproblems AT buttazzogiuseppe variationalmethodsinshapeoptimizationproblems |