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A stationary free boundary problem modeling a three-dimensional electrostaticMEMS device is investigated. The device is made of a rigid ground plate and anelastic top plate which is hinged at its boundary, the plates being held atdifferent voltages. The model couples a nonlocal fourth-order equation for thedeformation of the top plate to a Laplace equation for the electrostaticpotential in the free domain between the two plates. The strength of thecoupling is tuned by a parameter $\lambda$ which is proportional to the squareof the applied voltage difference. Existence of a stable stationary solution isestablished for small values of $\lambda$. Nonexistence of stationary solutionsis obtained when $\lambda$ is large enough.

On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case