Compensated compactness for nonlinear homogenization and reduction of dimension
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.
scientific article; zbMATH DE number 2123243