Methods and Applications of Analysis

Volume 15 (2008)

Number 3

Uniqueness of Solutions for an Elliptic Equation Modeling MEMS

Pages: 341 – 354



Pierpaolo Esposito

Nassif Ghoussoub


We show among other things, that for small voltage, the stable solution of the basic nonlinear eigenvalue problem modelling a simple electrostatic MEMS is actually the unique solution, provided the domain is star-shaped and the dimension is larger or equal than 3. In two dimensions, we need the domain to be either strictly convex or symmetric. The case of a power permittivity profile is also considered. Our results, which use an approach developed by Schaaf, extend and simplify recent results by Guo and Wei.


MEMS; stable solutions; quenching branch

2010 Mathematics Subject Classification

35B32, 35J20, 35J60

Published 1 January 2008