The General Theory of Homogenization (eBook)

The General Theoryof Homogenization 2
1 Why Do I Write? 22
2 A Personalized Overview of Homogenization I 43
3 A Personalized Overview of Homogenization II 59
4 An Academic Question of Jacques-Louis Lions 79
5 A Useful Generalization by François Murat 89
6 Homogenization of an Elliptic Equation 95
7 The Div–Curl Lemma 108
8 Physical Implications of Homogenization 115
9 A Framework with Differential Forms 122
10 Properties of H-Convergence 130
11 Homogenization of Monotone Operators 145
12 Homogenization of Laminated Materials 153
13 Correctors in Linear Homogenization 162
14 Correctors in Nonlinear Homogenization 171
15 Holes with Dirichlet Conditions 180
16 Holes with Neumann Conditions 189
17 Compensated Compactness 196
18 A Lemma for Studying Boundary Layers 206
19 A Model in Hydrodynamics 214
20 Problems in Dimension N = 2 221
21 Bounds on Effective Coefficients 232
22 Functions Attached to Geometries 243
23 Memory Effects 256
24 Other Nonlocal Effects 271
25 The Hashin–Shtrikman Construction 286
26 Confocal Ellipsoids and Spheres 301
27 Laminations Again, and Again 318
28 Wave Front Sets, H-Measures 327
29 Small-Amplitude Homogenization 351
30 H-Measures and Bounds on Effective Coefficients 362
31 H-Measures and Propagation Effects 370
32 Variants of H-Measures 385
33 Relations Between Young Measuresand H-Measures 408
34 Conclusion 429
35 Biographical Information 442
36 Abbreviations and Mathematical Notation 447
References 455
Index 462