A variational approach to a stationary free boundary problem modeling MEMS
ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 2, pp. 417-438.

A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid ground plate. The model couples a non-local fourth-order equation for the elastic plate deflection to the harmonic electrostatic potential in the free domain between the elastic and the ground plate. The corresponding energy is non-coercive reflecting an inherent singularity related to a possible touchdown of the elastic plate. Stationary solutions are constructed using a constrained minimization problem. A by-product is the existence of at least two stationary solutions for some values of the applied voltage.

Received:
DOI: 10.1051/cocv/2015012
Classification: 35J35, 35R35, 35Q74
Keywords: MEMS, free boundary, stationary solutions, multiplicity, constrained minimization
Laurençot, Philippe 1; Walker, Christoph 2

1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, 31062 Toulouse cedex 9, France.
2 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany.
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Laurençot, Philippe; Walker, Christoph. A variational approach to a stationary free boundary problem modeling MEMS. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 2, pp. 417-438. doi : 10.1051/cocv/2015012. http://archive.numdam.org/articles/10.1051/cocv/2015012/

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