Abstract
AbstractA two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the deflection of the plate is derived. The latter paves the way for the construction of energy minimizers and also provides the Euler–Lagrange equation satisfied by these minimizers. A by-product is the monotonicity of the electrostatic energy with respect to the deflection.
Funder
Gottfried Wilhelm Leibniz Universität Hannover
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference7 articles.
1. Henrot, A., Pierre, M.: Shape Variation and Optimization, vol. 28 of EMS Tracts in Mathematics. European Mathematical Society (EMS), Zürich (2018)
2. Laurençot, Ph., Nik, K., Walker, Ch.: Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties. Calculus of Variations and Partial Differential Equations 61, pp. 1–51. Id/No 16 (2022)
3. Laurençot, Ph., Walker, Ch.: Heterogeneous dielectric properties in models for microelectromechanical systems. SIAM J. Appl. Math. 78, 504–530 (2018)
4. Laurençot, Ph., Walker, Ch.: Shape derivative of the Dirichlet energy for a transmission problem. Arch. Ration. Mech. Anal. 237, 447–496 (2020)
5. Laurençot, Ph., Walker, Ch.: $${H}^2$$-regularity for a two-dimensional transmission problem with geometric constraint. Math. Z. 322, 1879–1904 (2022)