On a free boundary model for three-dimensional MEMS with a hinged top plate: stationary case (Q2244856)

Summary: 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. For Part II, see [the author, Commun. Pure Appl. Anal. 20, No. 10, 3395--3417 (2021; Zbl 1479.35517)].