Abstract
47 Braides, A., Correctors for the homogenization of almost periodic monotone operators, Asymptotic Analysis 5 (1991) 47-74. In a previous paper (Braides et aI., 1990) it has been proven, under very mild almost periodicity conditions, that we have weak convergence in HI.p(.Q) of the solutions u, of boundary problems in an open set .Q related to the quasi-linear monotone operator -div(a(x/f, Du,)), to a function u, which solves an analogous problem related to a homogenized operator div(b(Du)). In general we do not have strong convergence of Du, to Du in (LP(.Q))n, even in the linear periodic case. It is possible however (Theorems 2.1 and 4.2) to express Du, in terms of Du, up to a rest converging strongly to 0 in (LP(.Q))n, applying correctors built up exploiting only the geometric properties of a. In the last section, we use the correctors result to obtain a homogenization theorem for quasi-linear equations with natural growth terms.
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