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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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