The general theory of homogenization: a personalized introduction/
Luc Tartar
- New York: Springer, 2009.
- xxii, 470 p. ; 24 cm.
- (Lecture notes of the Unione Matematica Italiana), 7 .
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 François Murat -- Homogenization of an elliptic equation -- The div-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 N=2 -- Bounds on effective coefficients -- Functions attached to geometries -- Memory effects -- Other nonlocal effects -- The Hashin-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.