The General Theory of Homogenization

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.

From the reviews:

"The book is divided in 34 short chapters including the introduction and a conclusion. ... Each chapter ends with some historical details on the mathematical authors who have been cited in the chapter. The book is surely interesting both from the mathematical point of view ... and for the historical background on homogenization theory, including H-convergence and Young measures. ... many mathematicians will learn how to use the key tools and to develop the basic but deep tools which can be used within this context." (Alain Brillard, Zentralblatt MATH, Vol. 1188, 2010)

"In his book Luc Tartar 're-animates' the historical genesis of one of the most important ideas in mathematical analysis of the last century, leading to a general theory of homogenization ... . a treasure trove for all those working in the field and those who want to get acquainted with it. ... it encourages young researchers to build on the material offered and develop new ideas. ... he or she will appreciate the author's effort to give a 'full' and perhaps necessarily personalized picture." (Guenter Leugering, Mathematical Reviews, Issue 2011 c)