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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 which is proportional to the square of the applied voltage difference. Existence of a stable stationary solution is established for small values of . Nonexistence of stationary solutions is obtained when is large enough.
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Katerina Nik, On a free boundary model for three-dimensional MEMS with a hinged top plate: Stationary case. Port. Math. 78 (2021), no. 2, pp. 211–232DOI 10.4171/PM/2067