Qualitative analysis of a curvature equation modelling MEMS with vertical loads. (October 2020) - Corsato, Chiara; De Coster, Colette; Obersnel, Franco; Omari, Pierpaolo
Abstract: We investigate existence, multiplicity and qualitative properties of the solutions of the Dirichlet problem for the singularly perturbed prescribed mean curvature equation − ( 1 − b u ) div ( ∇ u 1 + | ∇ u | 2 ) = a ( u − R ) 2 + b 1 + | ∇ u | 2, in Ω, u = 0, on ∂ Ω, where a, b, R are given constants and Ω is a bounded regular domain in R N . This model appears in the theory of micro-electro-mechanical systems (MEMS) when the effects of capillarity and vertical forces are taken into account.