Stationary solutions to a nonlocal fourth-order elliptic obstacle problem

Philippe Laurençot (1) , Christoph Walker

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Existence of stationary solutions to a nonlocal fourth-order elliptic obstacle problem arising from the modelling of microelectromechanical systems with heterogeneous dielectric properties is shown. The underlying variational structure of the model is exploited to construct these solutions as minimizers of a suitably regularized energy, which allows us to weaken considerably the assumptions on the model used in a previous article.

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurençot, Christoph Walker. Stationary solutions to a nonlocal fourth-order elliptic obstacle problem. Journal of Elliptic and Parabolic Equations, 2020, 6, pp.171--186. ⟨10.1007/s41808-020-00059-9⟩. ⟨hal-02495084⟩