Qualitative analysis of a curvature equation modelling MEMS with vertical loads. (October 2020)

• Record Type: Journal Article
• Authors: Corsato, Chiara; De Coster, Colette; Obersnel, Franco; Omari, Pierpaolo
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Prescribed mean curvature equation -- Dirichlet boundary condition -- Classical solution -- Generalized solution -- Existence -- Multiplicity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103123
• Languages: English
• ISSNs: 1468-1218

Abstract

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.