Uniqueness of solutions for an elliptic equation modeling MEMS

Details Uniqueness of solutions for an elliptic equation modeling MEMS Uniqueness of solutions for an elliptic equation modeling MEMS

2008-10-07

arxiv.org/abs/0810.1257v1

Mathematics

Analysis of PDEs

11 pages. Updated versions --if any-- of this author's papers can be downloaded at http://www.birs.ca/~nassif/

Scientific paper

We study the effect of the parameter $\lambda$, the dimension $N$, the profile $f$ and the geometry of the domain $\Omega \subset\mathbb{R}^N$, on the question of uniqueness of the solutions to the following elliptic boundary value problem with a singular nonlinearity: $$ 180pt {{array}{ll} -\Delta u= \frac{\lambda f(x)}{(1-u)^2} & \hbox{in}\Omega 0

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