G-Convergence and Homogenization of Nonlinear Partial Differential Operators

This volume deals with G-convergence and homogenization for various classes of nonlinear partial differential operators. Chapter 1 is devoted to some preliminary issues from nonlinear analysis as well as to G-convergence of abstract operators, including the case of abstract parabolic operators. Chapter 2 introduces details of the notion of strong G-convergence for nonlinear second order elliptic operators in divergence form, and in Chapter 3 the homogenization problem for rapidly oscillated nonlinear random homogenous elliptic operators is dealt with. On the basis of these results, almost periodic and periodic cases are studied. Finally, in Chapter 4, some of the previous results are extended to the case of nonlinear parabolic operators. The volume concludes with two appendices, one of which is devoted to homogenization of nonlinear difference schemes, while the other lists some open problems of relevance, and a bibliography.