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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Κύριος συγγραφέας: Tartar, Luc (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
Σειρά:Lecture Notes of the Unione Matematica Italiana, 7
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • 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.