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A model for a MEMS device, consisting of a fixed bottom plate and an elasticplate, is studied. It was derived in a previous work as a reinforced limit whenthe thickness of the insulating layer covering the bottom plate tends to zero.This asymptotic model inherits the dielectric properties of the insulatinglayer. It involves the electrostatic potential in the device and thedeformation of the elastic plate defining the geometry of the device. Theelectrostatic potential is given by an elliptic equation with mixed boundaryconditions in the possibly non-Lipschitz region between the two plates. Thedeformation of the elastic plate is supposed to be a critical point of anenergy functional which, in turn, depends on the electrostatic potential due tothe force exerted by the latter on the elastic plate. The energy functional isshown to have a minimizer giving the geometry of the device. Moreover, thecorresponding Euler-Lagrange equation is computed and the maximal regularity ofthe electrostatic potential is established.

Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties