Homogenization of differential operators and integral functionals:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1994
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005913235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus dem Russ. übers. |
| Umfang: | XI, 570 S. Ill., graph. Darst. |
| ISBN: | 0387548092 3540548092 9783642846618 |
Internformat
MARC
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| 100 | 1 | |a Žikov, Vasilij V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Homogenization of differential operators and integral functionals |c V. V. Jikov ; S. M. Kozlov ; O. A. Oleinik |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a XI, 570 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 700 | 1 | |a Kozlov, Sergej M. |e Verfasser |4 aut | |
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Datensatz im Suchindex
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|---|---|
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| adam_text | Table of Contents
Chapter 1
Homogenization of Second Order Elliptic Operators
with Periodic Coefficients 1
1.1 Preliminaries 1
1.2 Setting of the Homogenization Problem 12
1.3 Problems of Justification; Further Examples 19
1.4 The Method of Asymptotic Expansions 24
1.5 Explicit Formulas for the Homogenized Matrix in the
Two Dimensional Case 35
1.6 Estimates and Approximations for the Homogenized Matrix . . 39
1.7 The Rayleigh Maxwell Formulas 45
Comments 53
Chapter 2
An Introduction to the Problems of Diffusion 55
2.1 Homogenization of Parabolic Operators 55
2.2 Homogenization and the Central Limit Theorem 61
2.3 Stabilization of Solutions of Parabolic Equations 64
2.4 Diffusion in a Solenoidal Flow 68
2.5 Diffusion in an Arbitrary Periodic Flow 73
2.6 Spectral Approach to the Asymptotic Problems of Diffusion . . 76
2.7 Diffusion with Absorption 83
Comments 84
Chapter 3
Elementary Soft and Stiff Problems 86
3.1 Homogenization of Soft Inclusions 86
3.2 Homogenization of Stiff Inclusions 96
3.3 Virtual Mass 106
3.4 The Method of Asymptotic Expansions 109
3.5 On a Dense Cubic Packing of Balls 112
3.6 The Dirichlet Problem in a Perforated Domain 119
Comments 131
viii Table of Contents
Chapter 4
Homogenization of Maxwell Equations 133
4.1 Preliminary Results 133
4.2 A Lemma on Compensated Compactness 138
4.3 Homogenization 141
4.4 The Problem of an Artificial Dielectric 145
Comments 148
Chapter 5
G Convergence of Differential Operators 149
5.1 Basic Properties of G Convergence 149
5.2 A Sufficient Condition of G Convergence 156
5.3 G Convergence of Abstract Operators 160
5.4 Compactness Theorem and Its Implications 163
5.5 G Convergence and Duality 166
5.6 Stratified Media 168
5.7 G Convergence of Divergent Elliptic Operators
of Higher Order 179
Comments 186
Chapter 6
Estimates for the Homogenized Matrix 187
6.1 The Hashin Shtrikman Bounds 187
6.2 Attainability of Bounds. The Hashin Structure 195
6.3 Extremum Principles 199
6.4 The Variational Method 202
6.5 G—Limit Media; Attainment of the Bounds on Stratified
Composites 205
6.6 The Method of Quasi Convexity 210
6.7 The Method of Null Lagrangians 212
6.8 The Method of Integral Representation 217
Comments 220
Chapter 7
Homogenization of Elliptic Operators with Random
Coefficients 222
7.1 Probabilistic Description of Non Homogeneous Media 223
7.2 Homogenization 227
7.3 Explicit Formulas in Two Dimensional Problems 233
7.4 Homogenization of Almost Periodic Operators 238
7.5 The General Theorem of Individual Homogenization 242
Comments 248
Table of Contents ix
Chapter 8
Homogenization in Perforated Random Domains 250
8.1 Homogenization 252
8.2 Remarks on Positive Definiteness of the Homogenized Matrix . . 264
8.3 Central Limit Theorem 268
8.4 Disperse Media 279
8.5 Criterion of Pointwise Stabilization; A Refinement
of the Central Limit Theorem 281
8.6 Stiff Problem for a Random Spherical Structure 284
8.7 Random Spherical Structure with Small Concentration 287
Comments 296
Chapter 9
Homogenization and Percolation 298
9.1 Existence of the Effective Conductivity 299
9.2 Random Structure of Chess Board Type 304
9.3 The Method of Percolation Channels 308
9.4 Conductivity Threshold for a Random Cubic Structure in 1R3 . 313
9.5 Resistance Threshold for a Random Cubic Structure in H3 . . . 318
9.6 Central Limit Theorem for Random Motion in an Infinite
Two Dimensional Cluster 319
Comments 321
Chapter 10
Some Asymptotic Problems for a Non Divergent Parabolic
Equation with Random Stationary Coefficients 323
10.1 Preliminary Remarks 323
10.2 Auxiliary Equation A*p = 0 on a Probability Space 325
10.3 Homogenization and the Central Limit. Theorem 330
10.4 Criterion of Pointwise Stabilization 332
Comments 336
Chapter 11
Spectral Problems in Homogenization Theory 338
11.1 Spectral Properties of Abstract Operators Forming a Sequence . 338
11.2 On the Spectrum of G Convergent Operators 345
11.3 The Sturm Liouville Problem 349
11.4 Spectral Properties of Stratified Media 355
11.5 Density of States for Random Elliptic Operators 357
11.6 Asymptotics of the Density of States 359
Comments 365
x Table of Contents
Chapter 12
Homogenization in Linear Elasticity 367
12.1 Some General Facts from the Theory of Elasticity 367
12.2 G Convergence of Elasticity Tensors 372
12.3 Homogenization of Periodic and Random Tensors 375
12.4 Fourth Order Operators 381
12.5 Linear Problems of Incompressible Elasticity 382
12.6 Explicit Formulas for Two Dimensional Incompressible
Composites 386
12.7 Some Questions of Analysis on a Probability Space 389
Chapter 13
Estimates for the Homogenized Elasticity Tensor 391
13.1 Basic Estimates 392
13.2 The Variational Method 395
13.3 Two Phase Media; Attainability of Bounds on Stratified
Composites 399
13.4 On the Hashin Structure 403
13.5 Disperse Media with Inclusions of Small Concentration 406
13.6 Fourth Order Operators; Systems of Stokes Type 409
Comments 414
Chapter 14
Elements of the Duality Theory 415
14.1 Convex Functions 415
14.2 Integral Functional 420
14.3 On Two Types of Boundary Value Problems 423
14.4 Dual Boundary Value Problems 427
14.5 Extremal Relations 431
14.6 Examples of Regular Lagrangians 433
Comments 437
Chapter 15
Homogenization of Nonlinear Variational Problems 438
15.1 Random Lagrangians 438
15.2 Two Principal Lemmas 444
15.3 Homogenization Theorems 449
15.4 Applications to Boundary Value Problems
in Perforated Domains 452
15.5 Chess Lagrangians; Dychne s Formula 455
Comments 458
Table of Contents xi
Chapter 16
Passing to the Limit in Nonlinear Variational Problems 460
16.1 Definition of / Convergence of Lagrangians; Formulation
of the Compactness Theorems 460
16.2 Convergence of Energies and Minimizers 465
16.3 Proof of the Compactness Theorems 468
16.4 Two Examples: Ulam s Problem; Homogenization Problem . . . 476
16.5 Compactness of Lagrangians in Plasticity Problems;
Application to L1 Closedness 480
16.6 Remarks on Non Convex Functionals 487
Comments 490
Chapter 17
Basic Properties of Abstract F Convergence 492
17.1 / Convergence of Functions on a Metric Space 492
17.2 T Convergence of Functions Denned in a Banach Space 495
17.3 / Convergence of Integral Functionals 498
Comments 501
Chapter 18
Limit Load 502
18.1 The Notion of Limit Load 502
18.2 Dual Definition of Limit Load 507
18.3 Equivalence Principle 509
18.4 Convergence of Limit Loads in Homogenization Problems .... 512
18.5 Surface Loads 518
18.6 Representation of the Functional F on BV0 521
18.7 / Convergence in BV0 529
Comments 534
Appendix A. Proof of the Nash Aronson Estimate 536
Appendix B. Weak Convergence in L1 and Weak Convergence
of Measures 540
Appendix C. A Property of Bounded Lipschitz Domains 542
References 544
Subject Index 569
|
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| id | DE-604.BV008959007 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:29:28Z |
| institution | BVB |
| isbn | 0387548092 3540548092 9783642846618 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005913235 |
| oclc_num | 260153262 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-12 DE-29T DE-384 DE-20 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
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| physical | XI, 570 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Žikov, Vasilij V. Kozlov, Sergej M. Olejnik, Olʹga A. 1925-2001 Homogenization of differential operators and integral functionals Homogenisierungsmethode (DE-588)4257770-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Homogenisieren (DE-588)4138007-1 gnd |
| subject_GND | (DE-588)4257770-6 (DE-588)4044779-0 (DE-588)4138007-1 |
| title | Homogenization of differential operators and integral functionals |
| title_auth | Homogenization of differential operators and integral functionals |
| title_exact_search | Homogenization of differential operators and integral functionals |
| title_full | Homogenization of differential operators and integral functionals V. V. Jikov ; S. M. Kozlov ; O. A. Oleinik |
| title_fullStr | Homogenization of differential operators and integral functionals V. V. Jikov ; S. M. Kozlov ; O. A. Oleinik |
| title_full_unstemmed | Homogenization of differential operators and integral functionals V. V. Jikov ; S. M. Kozlov ; O. A. Oleinik |
| title_short | Homogenization of differential operators and integral functionals |
| title_sort | homogenization of differential operators and integral functionals |
| topic | Homogenisierungsmethode (DE-588)4257770-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Homogenisieren (DE-588)4138007-1 gnd |
| topic_facet | Homogenisierungsmethode Partielle Differentialgleichung Homogenisieren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005913235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Teilbibliothek Mathematik & Informatik
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