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September 2008 Uniqueness of Solutions for an Elliptic Equation Modeling MEMS
Pierpaolo Esposito, Nassif Ghoussoub
Methods Appl. Anal. 15(3): 341-354 (September 2008).


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.


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Pierpaolo Esposito. Nassif Ghoussoub. "Uniqueness of Solutions for an Elliptic Equation Modeling MEMS." Methods Appl. Anal. 15 (3) 341 - 354, September 2008.


Published: September 2008
First available in Project Euclid: 10 April 2009

zbMATH: 1171.35044
MathSciNet: MR2500851

Primary: 35B32 , 35D10 , 35J20 , 35J60

Keywords: MEMS , quenching branch , stable solutions

Rights: Copyright © 2008 International Press of Boston

Vol.15 • No. 3 • September 2008
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