The General Theory of Homogenization A Personalized Introduction
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2010, 2010
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| Edition: | 1st ed. 2010 |
| Series: | Lecture Notes of the Unione Matematica Italiana
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Why Do I Write?
- A Personalized Overview of Homogenization I
- A Personalized Overview of Homogenization II
- An Academic Question of Jacques-Louis Lions
- A Useful Generalization by Fran#x00E7;ois Murat
- Homogenization of an Elliptic Equation
- The Div#x2013;Curl Lemma
- Physical Implications of Homogenization
- A Framework with Differential Forms
- Properties of H-Convergence
- Homogenization of Monotone Operators
- Homogenization of Laminated Materials
- Correctors in Linear Homogenization
- Correctors in Nonlinear Homogenization
- Holes with Dirichlet Conditions
- Holes with Neumann Conditions
- Compensated Compactness
- A Lemma for Studying Boundary Layers
- A Model in Hydrodynamics
- Problems in Dimension = 2
- Bounds on Effective Coefficients
- Functions Attached to Geometries
- Memory Effects
- Other Nonlocal Effects
- The Hashin#x2013;Shtrikman Construction
- Confocal Ellipsoids and Spheres
- Laminations Again, and Again
- Wave Front Sets, H-Measures
- Small-Amplitude Homogenization
- H-Measures and Bounds on Effective Coefficients
- H-Measures and Propagation Effects
- Variants of H-Measures
- Relations Between Young Measures and H-Measures
- Conclusion
- Biographical Information
- Abbreviations and Mathematical Notation