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arXiv · 0810.1257

Uniqueness of solutions for an elliptic equation modeling MEMS

Nassif Ghoussoub·Pierpaolo Esposito
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Abstract

We study the effect of the parameter $λ$, the dimension $N$, the profile $f$ and the geometry of the domain $Ω\subset\mathbb{R}^N$, on the question of uniqueness of the solutions to the following elliptic boundary value problem with a singular nonlinearity: $$ 180pt {{array}{ll} -Δu= \frac{λf(x)}{(1-u)^2} & \hbox{in}Ω0<u<1 &\hbox{in}Ωu=0 &\hbox{on}\partial Ω. {array}. 130pt (S)_{λ, f} $$ This equation has been proposed as a model for a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 below a rigid ground plate located at height z = 1.

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Nassif Ghoussoub, Pierpaolo Esposito. 2008-10-07. Uniqueness of solutions for an elliptic equation modeling MEMS. https://arxiv.org/abs/0810.1257

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