Laurençot, Philippe; Nik, Katerina; Walker, Christoph Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties. (English) Zbl 1481.35137 Calc. Var. Partial Differ. Equ. 61, No. 1, Paper No. 16, 51 p. (2022). Summary: A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This asymptotic model inherits the dielectric properties of the insulating layer. It involves the electrostatic potential in the device and the deformation of the elastic plate defining the geometry of the device. The electrostatic potential is given by an elliptic equation with mixed boundary conditions in the possibly non-Lipschitz region between the two plates. The deformation of the elastic plate is supposed to be a critical point of an energy functional which, in turn, depends on the electrostatic potential due to the force exerted by the latter on the elastic plate. The energy functional is shown to have a minimizer giving the geometry of the device. Moreover, the corresponding Euler-Lagrange equation is computed and the maximal regularity of the electrostatic potential is established. Cited in 1 Document MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J25 Boundary value problems for second-order elliptic equations 35Q74 PDEs in connection with mechanics of deformable solids 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35J20 Variational methods for second-order elliptic equations 49Q10 Optimization of shapes other than minimal surfaces 49J40 Variational inequalities Keywords:Laplace equation; mixed boundary conditions; existence and uniqueness; variational methods PDFBibTeX XMLCite \textit{P. Laurençot} et al., Calc. Var. Partial Differ. Equ. 61, No. 1, Paper No. 16, 51 p. (2022; Zbl 1481.35137) Full Text: DOI arXiv References: [1] Amann, H.; Escher, J., Analysis. III (2009), Basel: Birkhäuser Verlag, Basel · Zbl 1187.28001 [2] Ambati, V. R., Asheim, A., van den Berg, J. 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