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Compensated compactness for nonlinear homogenization and reduction of dimension. (English) Zbl 1072.35028
In this paper the authors study the limit behavior, as $$\varepsilon \rightarrow 0$$, of some nonlinear monotone equations in divergence form, in a domain $$\Omega^\varepsilon$$, which is thin in some directions (e.g. $$\Omega^\varepsilon$$ is a plate or a thin cylinder). After rescaling to a fixed domain the differential equation is transformed into an equation of the same type, but with the differential operator depending, in an opportune manner, by $$\varepsilon$$. With particular assumptions on the coefficients and a suitable compensated compactness, the authors prove a closure result, i.e. the limit problem has the same form. This applies in particular to the limit behaviour of nonlinear monotone equations in laminated plates.

MSC:
 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35Q72 Other PDE from mechanics (MSC2000) 74Q05 Homogenization in equilibrium problems of solid mechanics
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