Homogenization of multiple integrals:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
2007
|
| Ausgabe: | reprint. |
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 298 S. |
| ISBN: | 9780198502463 |
Internformat
MARC
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| 245 | 1 | 0 | |a Homogenization of multiple integrals |c Andrea Braides and Anneliese Defranceschi |
| 250 | |a reprint. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 2007 | |
| 300 | |a XIV, 298 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 12 | |
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| 830 | 0 | |a Oxford lecture series in mathematics and its applications |v 12 |w (DE-604)BV009910017 |9 12 | |
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Datensatz im Suchindex
| _version_ | 1804139392696057856 |
|---|---|
| adam_text | CONTENTS
Notation
xiii
Introduction
1
I LOWER SEMICONTINUITY OF INTEGRAL
FUNCTIONALS
1
Lower semicontinuity and coerciveness
11
1.1
Lower semicontinuity
11
1.2
Yosida transforms
13
1.3
Coerciveness conditions. The direct method
16
1.4
Exercises
17
2
Weak convergence
18
2.1
Weak convergence in Lebesgue spaces
18
2.2
Weak convergence in Sobolev spaces
22
2.3
Weak* convergence of measures
22
2.4
Weak compactness criteria in L1
24
2.5
Exercises
27
3
Minimum problems in Sobolev spaces
28
3.1
The direct method. An example of application
28
3.2
Borei
and
Carathéodory
functions
29
3.3
Rellich s Theorem and equivalent conditions for lower
semicontinuity
31
3.4
Exercises
32
4
Necessary conditions for weak lower semicontinuity
33
4.1
General necessary conditions
33
4.2
W1 p-quasiconvexity
34
4.3
Rank-l-convexity
40
4.4
Exercises
41
5
Sufficient conditions for weak lower semicontinuity
42
5.1
Convexity
42
5.2
Polyconvexity
45
5.3
Quasiconvexity
48
5.4
Exercises
52
6
The structure of quasiconvex functions
54
6.1
Quasiconvexity of polyconvex functions
54
6.2
Quasiconvexification
55
Contents
6.3
Example of a quasiconvex non-polyconvex function
59
6.4
Example of a rank-l-convex non-quasiconvex function
60
II r-CONVERGENCE
7
A naïve
introduction to F-convergence
65
7.1
Definition and basic properties
65
7.2
Lower and upper
Г
-limits
67
7.3
Further properties. Compactness
70
7.4
Exercises
72
8
The indirect methods of T-convergence
73
8.1
Г
-limits
and Yosida transforms
73
8.2
An example:
Г
-limits
of quadratic functionais
74
9
Direct methods. An integral representation result
77
9.1
Localization
77
9.2
Integral representation on Sobolev spaces
77
9.3
Integral representation of homogeneous functionais
81
10
Increasing set functions
82
10.1
Increasing set functions
82
10.2
A characterization of measures as set functions
82
10.3
Increasing set functions and compactness of
Г
-limits
84
11
The fundamental estimate
85
11.1
Fundamental estimates
85
11.2
Subadditivity of
Г
-limits
88
11.3
Г
-limits
and boundary values
90
11.4
Exercises
92
12
Integral functionais with standard growth conditions
93
12.1
Standard growth conditions
93
12.2
Fundamental estimate
93
12.3
Compactness for the
Г
-limits
95
12.4
Г
-limits
of homogeneous functionais
96
12.5
Exercises
98
III BASIC HOMOGENIZATION
13
A 1-dimensional example
101
13.1
The cell-problem homogenization formula
101
13.2
The asymptotic homogenization formula
103
13.3
Proof of the F-convergence
104
13.4
Exercises
106
14
Periodic homogenization
108
14.1
The asymptotic homogenization formula
109
Contents
14.2 The Homogenization Theorem
111
14.3
Convex
homogenization 114
14.3.1
The cell-problem formula
114
14.3.2
Non-coercive convex
homogenization 115
14.4
A counterexample to the cell-problem formula
120
14.5
An application: homogenization of elliptic equations in
divergence form
123
14.6
Exercises
125
15
Almost-periodic homogenization
128
15.1
Homogenization of uniformly almost-periodic funct-
ionals
128
15.2
An example: loss of smoothness by homogenization
135
15.3
Exercises
140
16
Two applications
142
16.1
Homogenization of Riemannian metrics
142
16.2
Homogenization of Hamilton Jacobi equations
145
17
A closure theorem for the homogenization
150
17.1
A closure theorem
150
17.2
An application: homogenization of Besicovitch almost-
periodic functionals
156
18
Loss of polyconvexity by homogenization
160
18.1
An example
160
IV FINER HOMOGENIZATION RESULTS
19
Homogenization of connected media
167
19.1
A homogenization theorem on periodic connected
domains
167
19.2
Convergence of Neumann boundary value problems
177
19.3
Convergence of Dirichlet boundary value problems
179
20
Homogenization with stiff and soft inclusions
181
20.1
Media with stiff and soft inclusions
181
20.2
The Homogenization Theorem
183
20.3
Convergence of minima
190
20.4
A Lavrentiev phenomenon
193
20.5
Loss of polyconvexity after homogenization
196
21
Homogenization with non-standard growth
conditions
199
21.1
A class of non-standard integrals
199
21.2
Convex homogenization
202
21.3
Non-convex homogenization
203
21.4
Exercises 212
Contents
22
Iterated
homogenization 214
22.1 Statement
of the Iterated Homogenization Theorem
214
22.2
Proof of the Iterated Homogenization Theorem
215
22.3
Exercises
222
23
Correctors for the homogenization
227
23.1
Convergence of momenta in homogenization
227
23.2
Definition and some properties of the correctors
234
23.3
Statement and proof of the correctors result
240
23.4
Correctors in the quasiperiodic case
246
23.5
Exercises
248
24
Homogenization of multi-dimensional structures
249
24.1
A smooth approach
249
24.2
A measure Sobolev-space approach
253
24.3
Homogenization of periodic thin structures
263
24.4
Exercises
268
V APPENDICES
A Almost-periodic functions
273
В
Construction of extension operators
277
С
Some regularity results
287
References
289
Notes to references
294
Index
297
|
| any_adam_object | 1 |
| author | Braides, Andrea 1961- Defranceschi, Anneliese |
| author_GND | (DE-588)120341735 |
| author_facet | Braides, Andrea 1961- Defranceschi, Anneliese |
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| author_sort | Braides, Andrea 1961- |
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| bvnumber | BV035684283 |
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| callnumber-raw | QA311 |
| callnumber-search | QA311 |
| callnumber-sort | QA 3311 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 660 |
| ctrlnum | (OCoLC)554049490 (DE-599)BVBBV035684283 |
| dewey-full | 515.624 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.624 |
| dewey-search | 515.624 |
| dewey-sort | 3515.624 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | reprint. |
| format | Book |
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| id | DE-604.BV035684283 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:43:22Z |
| institution | BVB |
| isbn | 9780198502463 |
| language | English |
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| owner_facet | DE-355 DE-BY-UBR DE-20 DE-83 |
| physical | XIV, 298 S. |
| publishDate | 2007 |
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| publishDateSort | 2007 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Braides, Andrea 1961- Verfasser (DE-588)120341735 aut Homogenization of multiple integrals Andrea Braides and Anneliese Defranceschi reprint. Oxford Clarendon Press 2007 XIV, 298 S. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 12 Homogenisierung Mathematik (DE-588)4403079-4 gnd rswk-swf Mehrfaches Integral (DE-588)4224692-1 gnd rswk-swf Funktionalintegral (DE-588)4155673-2 gnd rswk-swf Funktionalintegral (DE-588)4155673-2 s DE-604 Mehrfaches Integral (DE-588)4224692-1 s Homogenisierung Mathematik (DE-588)4403079-4 s 1\p DE-604 Defranceschi, Anneliese Verfasser aut Oxford lecture series in mathematics and its applications 12 (DE-604)BV009910017 12 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017738498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Braides, Andrea 1961- Defranceschi, Anneliese Homogenization of multiple integrals Oxford lecture series in mathematics and its applications Homogenisierung Mathematik (DE-588)4403079-4 gnd Mehrfaches Integral (DE-588)4224692-1 gnd Funktionalintegral (DE-588)4155673-2 gnd |
| subject_GND | (DE-588)4403079-4 (DE-588)4224692-1 (DE-588)4155673-2 |
| title | Homogenization of multiple integrals |
| title_auth | Homogenization of multiple integrals |
| title_exact_search | Homogenization of multiple integrals |
| title_full | Homogenization of multiple integrals Andrea Braides and Anneliese Defranceschi |
| title_fullStr | Homogenization of multiple integrals Andrea Braides and Anneliese Defranceschi |
| title_full_unstemmed | Homogenization of multiple integrals Andrea Braides and Anneliese Defranceschi |
| title_short | Homogenization of multiple integrals |
| title_sort | homogenization of multiple integrals |
| topic | Homogenisierung Mathematik (DE-588)4403079-4 gnd Mehrfaches Integral (DE-588)4224692-1 gnd Funktionalintegral (DE-588)4155673-2 gnd |
| topic_facet | Homogenisierung Mathematik Mehrfaches Integral Funktionalintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017738498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009910017 |
| work_keys_str_mv | AT braidesandrea homogenizationofmultipleintegrals AT defranceschianneliese homogenizationofmultipleintegrals |