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