Methods and Applications of Analysis
- Methods Appl. Anal.
- Volume 15, Number 3 (2008), 341-354.
Uniqueness of Solutions for an Elliptic Equation Modeling MEMS
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.
Methods Appl. Anal., Volume 15, Number 3 (2008), 341-354.
First available in Project Euclid: 10 April 2009
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Esposito, Pierpaolo; Ghoussoub, Nassif. Uniqueness of Solutions for an Elliptic Equation Modeling MEMS. Methods Appl. Anal. 15 (2008), no. 3, 341--354. https://projecteuclid.org/euclid.maa/1239396534