Homogenization of Differential Operators and Integral Functionals

This book is an extensive study of the theory of homogenization of partial differential equations. This theory has become increasingly important in the last two decades and it forms the basis for numerous branches of physics like the mechanics of composite and perforated materials, filtration and disperse media. It will become an indispensable reference for graduate students in mathematics, physics and engineering.

Inhalt
1 Homogenization of Second Order Elliptic Operators with Periodic Coefficients.- 2 An Introduction to the Problems of Diffusion.- 3 Elementary Soft and Stiff Problems.- 4 Homogenization of Maxwell Equations.- 5 G-Convergence of Differential Operators.- 6 Estimates for the Homogenized Matrix.- 7 Homogenization of Elliptic Operators with Random Coefficients.- 8 Homogenization in Perforated Random Domains.- 9 Homogenization and Percolation.- 10 Some Asymptotic Problems for a Non-Divergent Parabolic Equation with Random Stationary Coefficients.- 11 Spectral Problems in Homogenization Theory.- 12 Homogenization in Linear Elasticity.- 13 Estimates for the Homogenized Elasticity Tensor.- 14 Elements of the Duality Theory.- 15 Homogenization of Nonlinear Variational Problems.- 16 Passing to the Limit in Nonlinear Variational Problems.- 17 Basic Properties of Abstract ?-Convergence.- 18 Limit Load.- Appendix A. Proof of the Nash-Aronson Estimate.- Appendix C. A Property of Bounded Lipschitz Domains.- References.