Asymptotic analysis of boundary value problems for quasi-linear monotone operators

Abstract

By means of the notion of G-convergence introduced in [4] we deal with the limit behaviour, as h→+∞, of the solutions u_h to Neumann boundary value problems for quasi-linear monotone operators of the form A_hu=−div(a_h(x,Du_h)), and we also include in our analysis more general linear boundary conditions. Furthermore, we extend the homogenization result obtained in [6] to this case and the corresponding correctors studied in [7]. Finally, we deal with the asymptotic behaviour, as h→+∞, of the solutions u_h to quasi-linear equations −div(a_h(x,Du_h))=f on perforated domains Ω_h⊆Ω of Rⁿ with homogeneous Neumann boundary conditions on the holes, when the regularity assumptions on a_h required in [5] are dropped.