Uniqueness of Solutions for an Elliptic Equation Modeling MEMS
Pierpaolo Esposito and Nassif Ghoussoub
Source: Methods Appl. Anal. Volume 15, Number 3 (2008), 341-354.
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.
Primary Subjects: 35J60, 35B32, 35D10, 35J20
Keywords: MEMS; stable solutions; quenching branch
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Methods and Applications of Analysis
