Methods and Applications of Analysis

Uniqueness of Solutions for an Elliptic Equation Modeling MEMS

Pierpaolo Esposito and Nassif Ghoussoub

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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.

Article information

Methods Appl. Anal., Volume 15, Number 3 (2008), 341-354.

First available in Project Euclid: 10 April 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35B32: Bifurcation [See also 37Gxx, 37K50] 35D10 35J20: Variational methods for second-order elliptic equations

MEMS stable solutions quenching branch


Esposito, Pierpaolo; Ghoussoub, Nassif. Uniqueness of Solutions for an Elliptic Equation Modeling MEMS. Methods Appl. Anal. 15 (2008), no. 3, 341--354.

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