  This paper is concerned with the elliptic equation
  $-\Delta u=\frac{\lambda }{(a-u)^p}$ in a connected, bounded $C^2$ domain
$\Omega$ of $\mathbb{R}^N$
  subject to zero Dirichlet boundary conditions, where $\lambda>0$, $N\geq 1$,
$p>0$ and $a:\bar\Omega\to[0,1]$ vanishes at the boundary with the rate ${\rm
dist}(x,\partial\Omega)^\gamma$
  for $\gamma>0$.
  When $p=2$ and $N=2$, this equation models the closed Micro-Electromechanical
Systems devices, where the elastic membrane sticks the curved ground plate on
the boundary, but insulating on the boundary. The function $a$ shapes the
curved ground plate.
  Our aim in this paper is to study qualitative properties of minimal solutions
of this equation when $\lambda>0$, $p>0$
  and to show how the boundary decaying of $a$ works on the minimal solutions
and the pull-in voltage. Particularly, we give a complete analysis for the
stability of the minimal solutions.
