The General Theory of Homogenization

1. Why Do I Write?
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2. A Personalized Overview of Homogenization I
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3. A Personalized Overview of Homogenization II
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4. An Academic Question of Jacques-Louis Lions
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5. A Useful Generalization by François Murat
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6. Homogenization of an Elliptic Equation
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7. The Div–Curl Lemma
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8. Physical Implications of Homogenization
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9. A Framework with Differential Forms
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10. Properties of H-Convergence
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11. Homogenization of Monotone Operators
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12. Homogenization of Laminated Materials
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13. Correctors in Linear Homogenization
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14. Correctors in Nonlinear Homogenization
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15. Holes with Dirichlet Conditions
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16. Holes with Neumann Conditions
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17. Compensated Compactness
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18. A Lemma for Studying Boundary Layers
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19. A Model in Hydrodynamics
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20. Problems in Dimension N = 2
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21. Bounds on Effective Coefficients
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22. Functions Attached to Geometries
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23. Memory Effects
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24. Other Nonlocal Effects
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25. The Hashin–Shtrikman Construction
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26. Confocal Ellipsoids and Spheres
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27. Laminations Again, and Again
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28. Wave Front Sets, H-Measures
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29. Small-Amplitude Homogenization
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30. H-Measures and Bounds on Effective Coefficients
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31. H-Measures and Propagation Effects
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32. Variants of H-Measures
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33. Relations Between Young Measures and H-Measures
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34. Conclusion
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35. Biographical Information
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36. Abbreviations and Mathematical Notation
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Avainsanat: Mathematics, Partial Differential Equations, Mechanics, Engineering Fluid Dynamics