Contents Online
Methods and Applications of Analysis
Volume 15 (2008)
Number 3
Uniqueness of Solutions for an Elliptic Equation Modeling MEMS
Pages: 341 – 354
DOI: https://dx.doi.org/10.4310/MAA.2008.v15.n3.a6
Authors
Abstract
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.
Keywords
MEMS, stable solutions, quenching branch
2010 Mathematics Subject Classification
35B32, 35J20, 35J60
Published 1 January 2008