Homogenization of multiple integrals:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford
Clarendon Press
1998
|
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
12 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009198122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XIV, 298 S. |
| ISBN: | 019850246X 9780198502463 |
Internformat
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| 245 | 1 | 0 | |a Homogenization of multiple integrals |c Andrea Braides and Anneliese Defranceschi |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1998 | |
| 300 | |a XIV, 298 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Homogénéisation (équations différentielles) |2 ram | |
| 650 | 7 | |a Intégrales multiples |2 ram | |
| 650 | 7 | |a MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) |2 larpcal | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 492f 2014 A 2347 |
|---|---|
| DE-BY-TUM_katkey | 1998848 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040080117119 |
| _version_ | 1821934424359436289 |
| 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 Borel and Caratheodory 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 WliP quasiconvexity 34
4.3 Rank 1 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
x Contents
6.3 Example of a quasiconvex non polyconvex function 59
6.4 Example of a rank 1 convex non quasiconvex function 60
II T CONVERGENCE
7 A na ive introduction to F convergence 65
7.1 Definition and basic properties 65
7.2 Lower and upper F limits 67
7.3 Further properties. Compactness 70
7.4 Exercises 72
8 The indirect methods of F convergence 73
8.1 F limits and Yosida transforms 73
8.2 An example: F limits of quadratic functionals 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 functionals 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 F limits 84
11 The fundamental estimate 85
11.1 Fundamental estimates 85
11.2 Subadditivity of F limits 88
11.3 F limits and boundary values 90
11.4 Exercises 92
12 Integral functionals with standard growth conditions 93
12.1 Standard growth conditions 93
12.2 Fundamental estimate 93
12.3 Compactness for the F limits 95
12.4 F limits of homogeneous functionals 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 xi
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
xii 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
B Construction of extension operators 277
C 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 |
| author_role | aut aut |
| author_sort | Braides, Andrea 1961- |
| author_variant | a b ab a d ad |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA311 |
| callnumber-search | QA311 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 660 SK 600 |
| classification_tum | MAT 352f MAT 492f |
| ctrlnum | (OCoLC)39235531 (DE-599)BVBBV013477742 |
| 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 3624 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013477742 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:48:02Z |
| institution | BVB |
| isbn | 019850246X 9780198502463 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009198122 |
| oclc_num | 39235531 |
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| owner_facet | DE-29T DE-11 DE-188 DE-384 DE-20 DE-91G DE-BY-TUM |
| physical | XIV, 298 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spellingShingle | Braides, Andrea 1961- Defranceschi, Anneliese Homogenization of multiple integrals Oxford lecture series in mathematics and its applications ANÁLISE FUNCIONAL larpcal Analyse - Problèmes et exercices ram Coercitivité Fonction quasi-convexe Fonctions presque périodiques ram Homogénéisation (équations différentielles) ram Intégrales multiples ram MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) larpcal OPERADORES INTEGRAIS larpcal Sobolev, Espaces de ram Homogenization (Differential equations) Multiple integrals Funktionalintegral (DE-588)4155673-2 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd Mehrfaches Integral (DE-588)4224692-1 gnd |
| subject_GND | (DE-588)4155673-2 (DE-588)4403079-4 (DE-588)4224692-1 |
| 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 | ANÁLISE FUNCIONAL larpcal Analyse - Problèmes et exercices ram Coercitivité Fonction quasi-convexe Fonctions presque périodiques ram Homogénéisation (équations différentielles) ram Intégrales multiples ram MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) larpcal OPERADORES INTEGRAIS larpcal Sobolev, Espaces de ram Homogenization (Differential equations) Multiple integrals Funktionalintegral (DE-588)4155673-2 gnd Homogenisierung Mathematik (DE-588)4403079-4 gnd Mehrfaches Integral (DE-588)4224692-1 gnd |
| topic_facet | ANÁLISE FUNCIONAL Analyse - Problèmes et exercices Coercitivité Fonction quasi-convexe Fonctions presque périodiques Homogénéisation (équations différentielles) Intégrales multiples MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) OPERADORES INTEGRAIS Sobolev, Espaces de Homogenization (Differential equations) Multiple integrals Funktionalintegral Homogenisierung Mathematik Mehrfaches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009198122&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 |
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