The general theory of homogenization : a personalized introduction
 Responsibility
 Luc Tartar.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer : UMI, c2009.
 Physical description
 xxii, 470 p. ; 24 cm.
 Series
 Lecture notes of the Unione Matematica Italiana ; 7.
Access
Creators/Contributors
 Author/Creator
 Tartar, Luc.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Why Do I Write?. A Personalized Overview of Homogenization I. A Personalized Overview of Homogenization II. An Academic Question of JacquesLouis Lions. A Useful Generalization by Francois Murat. Homogenization of an Elliptic Equation. The DivCurl Lemma. Physical Implications of Homogenization. A Framework with Differential Forms. Properties of HConvergence. 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 HashinShtrikman Construction. Confocal Ellipsoids and Spheres. Laminations Again, and Again. Wave Front Sets, HMeasures. SmallAmplitude Homogenization. HMeasures and Bounds on Effective Coefficients. HMeasures and Propagation Effects. Variants of HMeasures. Relations Between Young Measures and HMeasures. Conclusion. Biographical Information. Abbreviations and Mathematical Notation.
 (source: Nielsen Book Data)
 Publisher's Summary
 Homogenization is not about periodicity, or Gammaconvergence, 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 topologies of weak type, the Gconvergence of Sergio Spagnolo, the Hconvergence of Francois Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author's Hmeasures, variants by Patrick Gerard, and others yet to be discovered.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2009
 Series
 Lecture notes of the Unione Matematica Italiana, 18629113 ; 7
 ISBN
 9783642051944
 3642051944
 9783642051951 (eISBN)
 3642051952 (eISBN)