Some homogenization and corrector results for nonlinear monotone operators

Abstract

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form − div (a (x, x/ε h, Du h)) = f h on Ω with Dirichlet boundary conditions. The sequence (ε h) tends to 0 and the map a(x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions. It is proved that u h → u weakly in (Formula presented.) where u is the solution of a homogenized problem − div(b(x, Du)) = f on Ω. We also prove some corrector results, i.e. we find (P h) such that Du h − P h(Du) → 0 in L 2(Ω, R n). © 1998 Taylor & Francis Group, LLC.