Abstract :

We study the limit behaviour of some nonlinear monotone partial differential equations, in a domain which is thin in some directions. The coefficients of these equations have special forms, well suited for reduction of dimension. After rescaling to a fixed domain, we prove a closure result, that is we prove that the limit problem has the same form as the rescaled one, under some compensated compactness condition. This applies in particular to the limit behaviour of nonlinear monotone equations in laminated plates.