  A stationary free boundary problem modeling a three-dimensional electrostatic
MEMS device is investigated. The device is made of a rigid ground plate and an
elastic top plate which is hinged at its boundary, the plates being held at
different voltages. The model couples a nonlocal fourth-order equation for the
deformation of the top plate to a Laplace equation for the electrostatic
potential in the free domain between the two plates. The strength of the
coupling is tuned by a parameter $\lambda$ which is proportional to the square
of the applied voltage difference. Existence of a stable stationary solution is
established for small values of $\lambda$. Nonexistence of stationary solutions
is obtained when $\lambda$ is large enough.
