Fin junction of ferroelectric thin films

In this paper, starting from a non-convex and nonlocal 3D-variational model for the electric polarization in a ferroelectric material, and using an asymptotic process based on dimensional reduction, we analyze junction phenomena for two orthogonal joined ferroelectric thin films. We obtain three different 2D-variational models for joined thin films, depending on how the reduction happens. Indeed, a memory effect of the reduction process appears, and it depends on the competition of the relative thickness of the two films. The guide parameter is the limit of the ratio between these two small thickness.