Dimensional reduction for the plate in elasticity on an unbounded domain

The dimensional reduction method is investigated for solving boundary value problems of the plate in elasticity on domain Ωd := R2 × (−d, d) by replacing the problems with systems of equations in R2. The basic tool to analyze the dimensional reduction technique for problems on an unbounded domain Ωd is the use of Fourier-transformation. The error estimates between the exact solution and the dimensionally reduced solution in a Hilbert space are obtained when d and N are given. The rates of convergence depends on the smoothness of the data on the faces.